Teaching the Mean Meaningfully

1996 ◽  
Vol 2 (2) ◽  
pp. 112-115
Author(s):  
John C. Uccellini
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Real Life ◽  
Pythagorean Theorem ◽  
School Students ◽  
Life Context ◽  
The Mean

Ask a group of middle school students what the average (mean) of 2, 8, 4, 6, 3, and 7 is; they will probably give the answer 5. Ask these same students what the number 5 represents in relationship to the six numbers given and the response usually heard is an explanation of the algorithm, “Add them up and divide by the number of them that you have.” The response is no different if the problem is given in a real-life context. For example, the foregoing six numbers could represent the number of pencils that six students have in their desks. In either situation, the almost universal response of students when questioned about the meaning of 5 from the “add and divide” algorithm demonstrates that students have not gained a conceptual understanding of this basic statistic. This same phenomenon exists throughout mathematics and is demonstrated whenever students try to explain subtraction by describing the vertical algorithm or the Pythagorean theorem by stating that c2 = a2 + b2. Through the use of simple manipulative activities and graphing, however, middle school students can be taught the mean meaningfully.

Changes in Middle School Students’ Motivation Toward Physical Education Over One School Year

2009 ◽  
Vol 28 (4) ◽  
pp. 378-399 ◽  
Author(s):  
Zan Gao ◽  
Amelia M. Lee ◽  
Melinda A. Solmon ◽  
Tao Zhang
Keyword(s):  
Middle School ◽  
Physical Education ◽  
Middle School Students ◽  
Self Efficacy ◽  
Educational Practice ◽  
Future Research ◽  
School Students ◽  
Task Values ◽  
The Mean ◽  
Over Time

This study investigated the relationships and mean-level changes of middle school students’ motivation (expectancy-related beliefs, task values, self-efficacy, and outcome expectancy) toward physical education over time, and how gender affected students’ motivation. Participants (N = 206) completed questionnaires over a 1-year period: once in the sixth and seventh grades and again in the seventh and eighth grades. Results yielded that self-efficacy and task values were positive predictors of students’ intention across cohorts. The mean levels of self-efficacy decreased over time for students in Cohort 1 (across sixth and seventh grades). However, results revealed a consistent decline in the mean levels of other motivational variables for both cohorts. No gender differences emerged for the variables. The findings are discussed in regard to the implications for educational practice, and future research areas are presented.

Developing Number Sense on the Number Line

2001 ◽  
Vol 6 (8) ◽  
pp. 448-451
Author(s):  
Jennifer M. Bay
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Young Children ◽  
Conceptual Understanding ◽  
Rational Numbers ◽  
Number Line ◽  
School Students ◽  
Large Numbers ◽  
Learning Mathematics ◽  
And Algebra

One of the most important lessons that I have learned as a teacher is that seemingly boring problems on paper can come alive if I can find a way to lift them off the page. This transformation took place when the number line in my classroom became a brightly colored rope that stretched the length of the room, held by a student at each end. I first saw this idea as an approach to help young children order numbers from 1 to 10, then adapted it for middle school students. The scope of the activity eventually expanded to include explorations of large numbers, rational numbers, and algebra. As I saw improvement in students' conceptual understanding and their enjoyment of the life-sized number line, I used it more often in my classroom. I also found that the activities with the number line involved communication, reasoning, and justification— important processes in learning mathematics (NCTM 1989, 2000).

Take Time for Action: Perimeter or Area? Which Measure Is It?

1999 ◽  
Vol 5 (1) ◽  
pp. 20-23
Author(s):  
Michaele F. Chappell ◽  
Denisse R. Thompson
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Physical Environment ◽  
Mathematics Curriculum ◽  
School Students ◽  
The Past ◽  
Fundamental Understanding ◽  
K 12

During the past twenty years, documents have recommended that the mathematics curriculum include measurement for all grades, K–12 (NCTM 1980, 1989). Indeed, students interact daily with measurement in their physical environment, for example, by finding the distance from home to school, their height and weight, and wall space for posters. Adolescents bring to the classroom varied conceptions of measurement, which may be in the form of basic applications or general formulas. All too often, a fundamental understanding of these ideas is sacrificed while students learn general formulas. This situation is particularly true for attributes of perimeter and area. To what extent do middle school students possess a conceptual understanding of these measurement concepts?

Teacher to Teacher: Truss(t)ing Triangles

1998 ◽  
Vol 3 (6) ◽  
pp. 394-396
Author(s):  
Bobbye Hoffman Bartels
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real Life ◽  
Seventh Grade ◽  
School Students ◽  
Mathematics Class ◽  
Traditional Mathematics ◽  
Saturday Academy ◽  
School Schedule ◽  
Rigidity Characteristic

Often middle school students see no connection between geometry and real life. The following activity was designed to help make this connection for seventh-grade students participating in a Saturday academy. The activity centers on an elementary investigation of the rigidity characteristic of triangles, a concept seldom mentioned in K-8 mathematic textbooks but essential to the construction of structures that have to absorb tremendous forces and not collapse. Although this activity was completed outside the traditional mathematics class, it can be adapted to a school schedule and completed over two or more class periods.

Polygon Capture: A Geometry Game

1998 ◽  
Vol 4 (2) ◽  
pp. 90-94
Author(s):  
William M. Carroll
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Sixth Grade ◽  
Fifth Grade ◽  
School Students ◽  
Problem Solving Skills ◽  
Evaluation Standards ◽  
Different Levels ◽  
School Curricula

The curriculum and evaluation standards for School Mathematics (NCTM 1989) calls for an increased role for geometry in the primary and middle school curricula. An important mathematical strand in its own right, geometry also provides opportunities to promote and assess mathematical communication, reasoning, and problem-solving skills. Unfortunately, many students lack the vocabulary and the conceptual understanding needed to desctibe geometric relationships. This atiicle describes a game, Capture the Polygons, that I have designed to help middle school students think about geometric properties and the relationships among them. A version of the game has been tested in firth- and sixth-grade classes as part of the field test of Fifth Grade Everyday Mathematics (Bell et al. 1995). Observations of classes playing the game, as well as feedback from their teachers, indicate that students find the game challenging but fun. Depending on the background of the students, it can be played at different levels of difficulty.

scholarly journals The Effectiveness of Using Narrative Approach in Teaching the Course of Interpretation (Tafseer) in Developing the First Intermediate Female Students’ Conceptual Understanding

2021 ◽  
Vol 32 (4) ◽  
pp. 1-19
Author(s):  
Siham bint Shuja Al-Harby
Keyword(s):  
Middle School ◽  
Conceptual Understanding ◽  
First Grade ◽  
Female Students ◽  
Control Group ◽  
Narrative Approach ◽  
School Students ◽  
Significance Level ◽  
The Mean ◽  
Experimental Group

This study aims at examining the effectiveness of using the narrative approach in teaching the Interpretation of the Qur'an course in the development of conceptual comprehension among first-grade middle school female students. To achieve the objective of this study, a quantitative quasi-experimental design has been used. The sample consisted of first-grade middle school female students at "the third middle school" in Buraidah city, as this school suits the objective of the study. A test of conceptual understanding has been built by the researchers according to a list of conceptual understating skills at a significance level of α ≤ 0.05. Results have shown that there are statistically significant differences at the level (α ≤ 0,05) between the mean scores of the experimental group and the control group students regarding the conceptual comprehension test in favour of the experimental group. Moreover, there are statistically significant differences between the mean scores of the experimental group students in the pre- and post-conceptual comprehension tests in favour of the post-test. Based on these results, the researchers have provided a set of related recommendations and suggestions, such as: accentuating the importance of using the narrative approach in constructing Sharia sciences courses in general and the interpretation of the Qur'an course in particular. Accordingly, the researchers have recommended conducting a study entitled the effectiveness of using the narrative approach in teaching the interpretation of the Qur'an course in developing the first-grade secondary school students’ conceptual comprehension.

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