Good Instruction in Mathematics

2020 ◽  
pp. 47-77
Author(s):  
George A. Khachatryan
Keyword(s):  
Mathematics Instruction ◽  
Instructional Methods ◽  
Cognitive Engagement ◽  
Discovery Learning ◽  
Trial And Error ◽  
Mutual Support ◽  
Instructional Programs ◽  
Good Mathematics Instruction ◽  
General Guidance

This chapter applies the lessons of Chapter 1 (which discusses how to identify good instruction) to the case of mathematics. There has been much controversy about what makes for good instruction in mathematics. Nevertheless, scientific and humanistic sources do allow us to paint a picture. Some instructional methods are less guided (such as pure discovery learning) and others more guided (like teacher-led instruction); scientific and humanistic evidence are in agreement that general guidance is needed, but should not come at the expense of student cognitive engagement. The evidence also consistently shows that instruction should emphasize genuine understanding of the underlying reasons for mathematical principles. Skills (such as fluency in computations) are not in opposition to concepts, but rather in mutual support. Solving varied and unexpected problems is essential in good mathematics instruction. Mathematical “rigor” (meaning precision in expression) plays an important role in mathematical thought, but should be carefully balanced with accessibility for children. While such principles give general guidance, knowing them is not enough to create excellent instructional programs: they need to be applied consistently in each moment of each lesson. Getting these details right is challenging, and can only be done through years of trial and error. This helps explain why good instructional traditions in mathematics are so rare.

Integrating Manipulatives and Computers in Problem-Solving Experiences

1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Good Mathematics Instruction ◽  
K 12

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.

Teaching Mathematics with Technology: Common Multiples: Activities on and off the Computer

1987 ◽  
Vol 35 (4) ◽  
pp. 35-37
Author(s):  
Robert J. Jensen
Keyword(s):  
Mathematics Instruction ◽  
Mathematical Concept ◽  
Teaching Mathematics ◽  
Good Mathematics Instruction ◽  
Traditional Representation

One feature of good mathematics instruction is to present students with a number of environments that embody the same concept but from different perspectives. Such multiple embodiments permit students to reflect on a particular mathematical concept and form generalizations about aspects of the concept that remain unchanged across representations. Also, particular aspects of an alternate embodiment may allow students to form an understanding that they may not have acquired through their first exposure to the content in its most traditional representation. This month's department offers two alternate representations for the concept of common multiples that can be modeled either on or off the computer.

“State standards and IEP goals. A lot of TPT products.” What Early Childhood Educators Report Using to Plan Mathematics Instruction

2020 ◽  
Author(s):  
Corey Peltier ◽  
Tiffany K Peltier ◽  
Taylor Werthen ◽  
Andy Heuer
Keyword(s):  
Special Education ◽  
Early Childhood ◽  
Special Education Teachers ◽  
Mathematics Instruction ◽  
State Standards ◽  
Early Childhood Educators ◽  
Future Research ◽  
Exceptional Children ◽  
What Works ◽  
What Works Clearinghouse

Access to high-quality resources is integral for educators to provide research-aligned mathematics instruction. Identifying the supplemental resources educators use to plan mathematics instruction can inform the ways researchers and organizations disseminate research-based practices. The goal of this study was to identify the frequency in which early childhood educators (i.e., pre-Kindergarten through third grade) reported using various resources to plan for mathematics instruction. Furthermore, we investigated whether differences were observed based on teacher factors (i.e., general or special education, route to certification, years of experience) and locale (i.e., rural, urban, suburban). We retained data from 917 teachers for data analysis. The three most frequently reported resources by educators were colleagues, Teachers Pay Teachers, and Google/Yahoo. The three least frequently reported resources were the typical outlets researchers use to reach teachers: What Works Clearinghouse, Teaching Exceptional Children, and Teaching Children Mathematics. General and special education teachers differed on their self-reported usage of five resources: colleagues, Google/Yahoo, teaching blogs, Teaching Exceptional Children, and the What Works Clearinghouse. Rural educators self-reported that they were less likely than suburban educators to use colleagues or specialists at the district to plan instruction. Implications for future research and practice are discussed.

Sign in / Sign up

Export Citation Format

Share Document