Proportional Reasoning: Lessons from Research in Data and Chance

2004 ◽  
Vol 10 (2) ◽  
pp. 104-109
Author(s):  
Jane Watson ◽  
J. Shaughnessy
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
Proportional Reasoning ◽  
School Mathematics ◽  
School Level ◽  
Principles And Standards ◽  
Middle School Level

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) places proportionality among the major concepts connecting different topics in the mathematics curriculum at the middle school level (p. 217). What concerns us about many of the problems presented to students, however, is that they are often posed purely as a ratio or proportion from the start. Often the statement of a problem is a giveaway that a proportion is involved. For example, the question “If 15 students out of 20 get a problem correct, how many students in a class of 28 would we expect to get the problem correct?” does not tap the depth of proportional reasoning that is required for meaningful problem solving.

Soundoff: Geometry: A Remedy for the Malaise of Middle School Mathematics

1989 ◽  
Vol 82 (9) ◽  
pp. 678-680
Author(s):  
Alfred S. Posamentier
Keyword(s):  
Middle School ◽  
Middle Grades ◽  
Mathematics Curriculum ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
School Level ◽  
Mathematics Educators ◽  
Arithmetic Teaching ◽  
Middle School Level

Many mathematics educators perceive that the weakest part of the precollege mathematics curriculum is at the middle school level, more specifically, the years immediately preceding the study of algebra. It seems that in the middle grades the development of mathematics has been put into a “holding pattern.” A quick glance at the curriculum for seventh and eighth grades—or in some cases sixth and seventh gradesshows that much arithmetic is still being taught. Haven't we, or shouldn't we have, completed teaching arithmetic in the previous five or six years? Indeed, how much arithmetic teaching do we need to do in an age of ever-improving calculators (Heid 1988)? Very often students greet a unit in these grades with the now famous comment, “Oh, I had this already.” “Sure,” thinks the teacher, “you may have had it, but have you learned it?” It is clear to many educators that these middle grades are key to turning a student “on” to or “off” from mathematics.

Spotlight on the Principles/Standards: Problem Solving in the Middle Grades

2000 ◽  
Vol 6 (2) ◽  
pp. 105-108
Author(s):  
Carol E. Malloy ◽  
D. Bruce Guild
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Middle Grades ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Measurement Algebra ◽  
Principles And Standards ◽  
Mathematical Relationships

IN WHAT WAYS WOULD YOU LIKE YOUR middle-grades students to experience problem solving in the mathematics curriculum? Do you want the curriculum to capture the excitement of geometry and measurement, algebra, statistics, and number relationships? Do you want it to help students understand and build new mathematical knowledge and explore new mathematical relationships? Do you want the curriculum to be filled with opportunities for students to ponder, create, and critique arguments about mathematics? If this is your vision for your students, then you should be pleased with, and excited by, the Problem Solving Standard in Principles and Standards for School Mathematics (NCTM 2000).

Birthdays and the Binary System: A Magical Mixture

1997 ◽  
Vol 3 (1) ◽  
pp. 6-12
Author(s):  
Karen S. Karp ◽  
Robert N. Ronau
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Binary System ◽  
School Mathematics ◽  
School Level ◽  
Birth Date ◽  
School Students ◽  
Evaluation Standards ◽  
System A ◽  
Middle School Level

Middle school students rank their birthday as being the most important day of the year for them and one that they eagerly anticipate, according to an informal poll. Teachers can capitalize on this interest by engaging them in the mathematical birth-date activities described in this article. Applications and tasks that are relevant to students' lives have been shown to motivate students at the middle school level, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Discovering Patterns in Pascal's Triangle

2019 ◽  
Vol 24 (4) ◽  
pp. 247-254
Author(s):  
Marilyn Howard
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
School Level ◽  
Blaise Pascal ◽  
Pascal’S Triangle ◽  
The Common ◽  
Pascal's Triangle ◽  
Common Era ◽  
Middle School Level

The less you know about the patterns in Pascal's triangle, the more fun you will have discovering the triangle's many secrets. I am amazed at how few students and even teachers (especially at the middle school level) have ever explored Pascal's triangle. Although this famous triangle bears the name of Blaise Pascal (1623-1662), who saw many of the patterns when he was only thirteen years old, it had been around for centuries before he was born. See the ancient diagram in figure 1, which appeared at the front of a Chinese book in 1303 (Vakil 2008). Evidence suggests that the properties of the elements of Pascal's triangle were known before the common era. Students and teachers alike can enjoy exploring patterns through problem solving with Pascal's triangle.

ONE POINT OF VIEW: Action for Middle Schoolers

1981 ◽  
Vol 28 (5) ◽  
pp. 2
Author(s):  
Joan Worth
Keyword(s):  
Middle School ◽  
Mathematics Curriculum ◽  
Point Of View ◽  
School Level ◽  
Policy Recommendations ◽  
Middle Schoolers ◽  
Middle School Level

The policy recommendations for the mathematics curriculum of the 1980s contained in An Agenda for Action* are most demanding, roost important, and therefore most exciting at the middle school level. For if many of the recommendations are going to be acted upon, that action will occur with middle schoolers, and the results could be dramatic.

Probability and the Seating Chart

1988 ◽  
Vol 81 (5) ◽  
pp. 393-397
Author(s):  
Dave Ptak
Keyword(s):  
Middle School ◽  
Decision Making ◽  
Problem Solving ◽  
School Level ◽  
Decision Making Processes ◽  
Basic Probability ◽  
Classroom Seating ◽  
Middle School Level

The problem-solving activities outlined here add to the collection of applications- at the middle school level and above- dealing with basic probability concepts. The context is an unusual and unexpected one: the classroom seating chart. Students need to know these concepts because they are at the heart of decision-making processes. Solving problems of the type that follow reinforces these concepts and gives students practice in the problem-solving techniques of counting, finding patterns, using diagrams, and generalizing.

scholarly journals Rural–Urban Differences in the Factors Affecting Depressive Symptoms among Older Adults of Two Regions in Myanmar

2021 ◽  
Vol 18 (6) ◽  
pp. 2818
Author(s):  
Yuri Sasaki ◽  
Yugo Shobugawa ◽  
Ikuma Nozaki ◽  
Daisuke Takagi ◽  
Yuiko Nagamine ◽  
...  
Keyword(s):  
Older Adults ◽  
Middle School ◽  
Depressive Symptoms ◽  
Rural Areas ◽  
Urban Areas ◽  
Depression Scale ◽  
Wealth Index ◽  
School Level ◽  
Cross Sectional ◽  
Middle School Level

The aim of the study was to investigate rural–urban differences in depressive symptoms in terms of the risk factors among older adults of two regions in Myanmar to provide appropriate intervention for depression depending on local characteristics. This cross-sectional study, conducted between September and December, 2018, used a multistage sampling method to recruit participants from the two regions, for face-to-face interviews. Depressive symptoms were assessed using the 15-item version of the Geriatric Depression Scale (GDS). Depressive symptoms were positively associated with living in rural areas (B = 0.42; 95% confidence interval (CI): 0.12,0.72), female (B = 0.55; 95% CI: 0.31,0.79), illness during the preceding year (B = 0.68; 95% CI: 0.45,0.91) and non-Buddhist religion (B = 0.57; 95% CI: 0.001,1.15) and protectively associated with education to middle school level or higher (B = −0.61; 95% CI: −0.94, −0.28) and the frequency of visits to religious facilities (B = −0.20; 95% CI: −0.30, −0.10). In women in urban areas, depressive symptoms were positively associated with illness during the preceding year (B = 0.78; 95% CI: 0.36, 1.20) and protectively associated with education to middle school level or higher (B = −0.67; 95% CI: −1.23, −0.11), middle or high wealth index (B = −0.92; 95% CI: −1.59, −0.25) and the frequency of visits to religious facilities (B = −0.20; 95% CI: −0.38, −0.03). In men in rural areas, illness during the preceding year was positively associated with depressive symptoms (B = 0.87; 95% CI: 0.33, 1.42). In women in rural areas, depressive symptoms were positively associated with illness during the preceding year (B = 0.83; 95% CI: 0.36, 1.30) and protectively associated with primary education (B = −0.62; 95% CI: −1.12, −0.12) and the frequency of visits to religious facilities (B = −0.44; 95% CI: −0.68, −0.21). Religion and wealth could have different levels of association with depression between older adults in the urban and rural areas and men and women. Interventions for depression in older adults should consider regional and gender differences in the roles of religion and wealth in Myanmar.

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