Using Attribute Blocks to Develop a Conceptual Understanding of Probability

2001 ◽  
Vol 6 (5) ◽  
pp. 290-294
Author(s):  
Robert J. Quinn
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Middle Grades ◽  
School Curriculum ◽  
Seventh Graders ◽  
Time Block ◽  
School Students ◽  
Formal Curriculum ◽  
Ability Levels

Middle school students continue to rely on concrete experiences to construct knowledge but are starting to develop the ability to think abstractly (NCTM 1989, p. 68). Thus, the middle school curriculum should provide a “bridge between the concrete elementary school curriculum and the more formal curriculum of the high school” (NCTM 1989, p. 102). This article describes a series of activities using attribute blocks designed to help middle school students construct knowledge about, and develop conceptual understanding of, probability. Depending on the ability levels of the students, these activities can be completed in a single twohour time block or can be spread over three or four sessions of about one hour each. These introductory probability explorations are appropriate for seventh graders but can be adapted for students at other levels. Attribute blocks are frequently used in the primary grades, but this article shows that they can be quite useful in the middle grades, as well.

Developing Conceptual Understanding of Relations and Functions with Attribute Blocks

1997 ◽  
Vol 3 (3) ◽  
pp. 186-190
Author(s):  
Robert J. Quinn
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Elementary Students ◽  
Conceptual Understanding ◽  
Middle Grades ◽  
School Curriculum ◽  
National Council ◽  
School Students ◽  
Formal Curriculum

Much attention has recently been focused on students in the middle grades. The unique difficulties and characteristics of this group have prompted the National Council of Teachers of Mathematics to refer to them as “children in transition” (NCTM 1989, 68). Middle school students continue to rely on concrete experiences to construct knowledge but are starting to develop the ability to think abtractly (NCTM 1989, 68). Thus, the middle school curriculum should build “a bridge between the concrete elementary school curriculum and the more formal curriculum of the high school” (NCTM 1989, 102). The series of lessons described in this article extends the concrete experiences that many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions.

Call for Manuscripts for the 1999 Focus Issue: Data and Chance in the Middle School Curriculum

1997 ◽  
Vol 3 (1) ◽  
pp. 45
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Mathematics Teaching ◽  
School Curriculum ◽  
School Students ◽  
Middle School Curriculum

The march 1999 issue of Mathematics Teaching in the Middle School (MTMS) will focus on the theme “Data and Chance in the Middle School Curriculum.” The Editorial Panel would like to feature exemplary lessons related to these topics, examine how these topics might be explored by middle school students, and highlight ways that data and chance can be connected to other areas of study.

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).

Socrates and the Three Little Pigs: Connecting Patterns, Counting Trees, and Probability

1999 ◽  
Vol 5 (3) ◽  
pp. 156-161
Author(s):  
Denisse R. Thompson ◽  
Richard A. Austin
Keyword(s):  
Middle School ◽  
South Carolina ◽  
New Jersey ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
School Curriculum ◽  
School Students ◽  
Middle School Curriculum ◽  
Curriculum Frameworks ◽  
Counting Trees

Explorations of concepts of chance should be a part of the middle school curriculum, as indicated in the mathematics curriculum frameworks developed by several states (Florida 1996; South Carolina 1993; New Jersey 1996). The challenge for teachers is to find contexts that interest middle school students and motivate them to explore these ideas.

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?

scholarly journals Virtual Manipulatives: A Tool to Support Access and Achievement With Middle School Students With Disabilities

2019 ◽  
Vol 35 (1) ◽  
pp. 51-59 ◽  
Author(s):  
Emily C. Bouck ◽  
Leslie A. Mathews ◽  
Corey Peltier
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Students With Disabilities ◽  
Middle Grades ◽  
Virtual Manipulatives ◽  
School Students ◽  
Content Areas ◽  
Mathematical Content ◽  
Concrete Manipulatives ◽  
Instructional Needs

Manipulatives offer students with disabilities access and support in classrooms. However, it is important for educators to be aware that concrete manipulatives are not the only option. Teachers serving students identified with a disability in the middle grades may consider selecting virtual manipulatives as supplement, complement, or in lieu of concrete manipulatives. In this technology in action, the authors provide information for educators about using virtual manipulatives and how they can be used across different settings, instructional needs, and mathematical content areas for middle school students with disabilities.

Using Models to Build an Understanding of Functions

2001 ◽  
Vol 6 (5) ◽  
pp. 310-318 ◽  
Author(s):  
Kathleen Cramer
Keyword(s):  
Middle School ◽  
Elementary School ◽  
Middle School Students ◽  
Middle Grades ◽  
Early Elementary ◽  
School Students ◽  
Early Elementary School

From the time that students enter kindergarten and throughout their early elementary school years, they should have multiple experiences exploring patterns. The study of patterns for middle school students should shift to the study of functions (NCTM 1989). The question that this article addresses is how to plan and organize instruction for middle-grades students to help them develop an understanding of function.

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.

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