Several years ago, when illinois issued its manuals describing the state's learning objectives in mathematics, one school district spent several months examining the mathematics curriculum from kindergarten through the twelfth grade. District goals were written by a committee, condensed to state goals, and submitted to the state as a learning-assessment plan. In the process, deficiencies in the district's curriculum were uncovered. A main deficiency concerned the amount and type of geometry taught in the middle grades.
John W. Dickey
MIDDLE-GRADE ARITHMETIC has made less change in recent years than has the primary-grade arithmetic; but the gains that have been made are in keeping with the newer philosophy of modern arithmetic. Modern textbooks on the teaching of a rithmetic, as well as the materials for the children, have also reflected these major changes in the philosophy, materials and methods. A brief look at the changes in content and methods is worthy of our attention.
Mary Lou DiPillo, Robert Sovchik and Barbara Moss
Not so long ago, writing was considered to be the exclusive domain of the English teacher. However, the current emphasis on subject integration has made writing a cross-curricular affair. Middle grades' students no longer write just in English class; they may find themselves writing in science, social studies, or mathematics class. In fact, involving students in the act of writing about mathematics is gaining widespread acceptance among teachers (Kliman and Richards 1992; Wilde 1991).
Welcome to the 2011 Focus Issue, which highlights connections between geometry and algebra that teachers can leverage in the middle grades. NCTM's Principles and Standards for School Mathematics (2000) recommends that students in the middle grades experience both the geometric representation of algebraic ideas and the algebraic representation of geometric ideas. By making these connections, students see that mathematical topics are related. They are not just a collection of isolated facts in seemingly disjoint fields but facts that often have many extensive connections.
Hari P. Koirala and Phillip M. Goodwin
A LARGE NUMBER OF MATHEMATICS EDUCATORS and teachers argue for including algebra in the middle school mathematics curriculum (Fouche 1997; Silver 1997). Recommended algebraic concepts to be taught in the middle grades include variable, expression, and equation (NCTM 1989), and middle-grade students should be able to “apply algebraic methods to solve a variety of real-world and mathematical problems” (NCTM 1989, 102). In spite of this emphasis on teaching algebra, a large number of middle school students, especially at the fifth- and sixthgrade levels, are never taught algebraic concepts.
Cynthia S. Lanius and Susan E. Williams
The mathematics studied in high school and beyond is organized around large themes, such as algebra, geometry, trigonometry, calculus, statistics, and so on. Even though the boundaries between these topics blur at times, the themes give connections and structure to the mathematics studied. For example, a huge body of knowledge is recognized as algebra. Students know that they are doing algebra when they formulate and solve equations, even when they perform these tasks in geometry or calculus class. In contrast, the study of mathematics in the middle grades, with the exception of prealgebra, lacks an overarching theme. Most middle-grades' courses, generally known merely as sixth-, seventh-, or eighth-grade mathematics, lack big ideas and tend to be a mass of discrete topics with little connection or continuity. The notion that prealgebra is a course to be done right before algebra, as opposed to a long-term theme to be developed over several years, is a prime example of this situation.
Gary Kader and Jim Mamer
The GAISE report emphasizes the importance of students having experience with statistical thinking throughout the pre-K-12 curriculum. Students' encounters with statistics in the middle grades should build on their foundational experiences from the elementary grades and provide a link to the inferential types of statistical thinking developed at the high school level. Middle-grades students should be actively involved in the statistical problem-solving process described in the GAISE report. That process involves (1) formulating a question that can be addressed with data, (2) collecting data to address the question, (3) analyzing the data, and (4) interpreting the results.
Fran Arbaugh, Carolyn Scholten and N. Kathryn Essex
“Spotlight on the Standards” focuses on the grades 6–8 content and process standards found in NCTM's Principles and Standards for School Mathematics (2000). The articles compare NCTM's Curriculum and Evaluation Standards for School Mathematics, published in 1989, with the Principles and Standards relating to the middle grades and suggest ways that teachers might incorporate Standards-based practices into their instruction.
Why Should We Use Literature to Teach Mathematics to Students in the Middle grades? There are compelling reasons for doing so. Literature can provide meaningful contexts in which students make sense of mathematics and construct their understandings of mathematical concepts. Well-chosen literature sparks interest and curiosity in students and increases their willingness to do mathematics; it also builds positive attitudes toward mathematics. The use of literature encourages communication and makes connections to other subjects as well as to topics within mathematics. Literature helps make mathematics relevant to students.
Carol E. Malloy and D. Bruce Guild
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).