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

1987 ◽  
Vol 35 (4) ◽  
pp. 35-37
Author(s):  
Robert J. Jensen

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.

2020 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Chinedu Victor Obasi

Mathematics is a human creation, which has been developing for more than four thousand years. It emerged as a response to different social and economic needs of civilizations. Historical development of mathematics stresses that mathematics as a science has always been connected to economic and social context and development of society. There is little or no research that promotes using historical content in mathematics lessons in the Nigeria context. In this paper, we model the use of history of mathematical thought (HMT) in mathematics instruction and solved the formulated model equation using integrating factor. The rate at which HMT is used by teachers in mathematics instruction is assumed to be proportional to the number of teachers that do not use HMT. The analysis suggests that with time, only a fraction of teachers can use HMT in teaching mathematics due to the fact that they will not remember to use it, and additional recruitment of teachers will result in only marginal improvement in the usage of HMT.


1991 ◽  
Vol 38 (6) ◽  
pp. 24-27
Author(s):  
Sue Goldstein ◽  
Frances A. Campbell

“I never seem to reach every student when I am teaching mathematics.” “There is never enough time for practicing mathematics skills.” These laments by typical elementary school teachers are both real and abundant. Teachers would love to have more time and more help to work with students individually on developing and mastering mathematics skills. Involving parents in working with their children in mathematics is a ready method of obtaining an extra resource for teachers when individualizing mathematics instruction.


2020 ◽  
Vol 10 (2) ◽  
pp. 38-42
Author(s):  
Eugen Ljajko

Teacher competencies are among the key factors of a successful mathematics instruction. The main goal of the study was to compare teachers' beliefs and attitudes affected by different strategies in organizing the instruction process. The study gives a comparison of teachers' competencies in three groups of teachers - one teaching mathematics without ICT, the second using ready-made GeoGebra applets and the third one developing their own GeoGebra applets in cooperation with their students. The survey includes 65 mathematics teachers working in 21 primary and secondary schools in southern regions of Serbia. We observed, assessed and compared affective-motivational characteristics of teachers - their beliefs and professional motivation. Results indicate that the teachers' affective-motivational characteristics depend on the way they employ technology in representing the content they teach. If the technology is used in an inappropriate manner it can impede the students' creativity, but it also obstructs teachers in deploying their full abilities in the process. The results also bring to the fore issues concerning ways to maintain positive effects achieved through ICT empowered instruction organized in the way the third group of teachers did.


2020 ◽  
Vol 122 (7) ◽  
pp. 1-44
Author(s):  
Jessica G. Rigby ◽  
Christine Andrews-Larson ◽  
I-Chien Chen

Background/Context When new, rigorous standards are adopted, teachers often need to learn new content and new ways of teaching while concurrently attending to accountability demands. Both formal and informal school structures potentially enable this new learning, and school leaders likely influence the nature of these structures. Purpose/Objective/Research Question/Focus of Study We examine teachers’ learning opportunities in one school by asking the following research questions: (1) What is the nature of changes in teachers’ formal learning opportunities, as seen by changes in teachers’ workgroup conversations about mathematics instruction? (2) In what ways do school leaders shape the nature of instructional conversations, and thus formal learning opportunities, in teacher workgroups? (3) What is the nature of changes in teachers’ informal opportunities to learn, as seen by shifts in informal advice networks? Research Design This is a longitudinal case study using mixed methods: qualitative analysis of audio-recorded teacher workgroup meetings and quantitative analysis of informal social networks. Data Collection and Analysis This analysis is a part of a larger eight-year longitudinal study, the Middle-school Mathematics and the Institutional Setting of Teaching (MIST). Data used in this analysis were collected over a three-year period in one middle school that was working to improve mathematics instruction by focusing on teaching mathematics conceptually and building procedural fluency. Data used in this analysis include audio-recorded teacher workgroup meetings, informal social network surveys, interview transcripts, and student-level standardized test scores. Findings/Results We found that formally, school leaders shifted teachers’ workgroup conversations away from instructional matters to those of standardized tests. Informally, teachers stopped going to each other for instructional advice. Triangulating interview data confirmed that over time, pressure that teachers felt to do well on the standardized tests shifted their attention away from a conceptual approach to instruction and toward an emphasis on test preparation. Conclusions/Recommendations Our findings suggest that school leaders must be involved in new learning about standards and instruction to appropriately support teachers’ learning opportunities.


2020 ◽  
pp. 47-77
Author(s):  
George A. Khachatryan

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.


1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown

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.


1991 ◽  
Vol 38 (7) ◽  
pp. 52-54
Author(s):  
John G. Harvey

No matter the level at which we teach mathematics, we are being asked to incorporate calculators into our instruction, to teach students both calculator facility and effective ways of using calculators, and to encourage and expect those students to use calculators appropriately. As early as 1975, just three years after the introduction of Texas Instruments's Data Math calculator, the National Advisory Committee on Mathematical Education (NACOME) urged that calculators be used in mathematics instruction (NACOME 1975, 40–43). Five years later the National Council of Teachers of Mathematics recommended that “mathematics programs [should] take full advantage of calculators … at all grade levels” (NCTM 1980, 1).


1994 ◽  
Vol 41 (9) ◽  
pp. 556-558
Author(s):  
Patrick W. Thompson ◽  
Diana Lambdin

Today we find common agreement that effective mathematics instruction in the elementary grades incorporates liberal use of concrete materials. Articles in the Arithmetic Teacher no longer exhort us to use concrete materials, nor does the Professional Standards for Teaching Mathematics (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.


1971 ◽  
Vol 64 (7) ◽  
pp. 627-628

The IMS program for teaching mathematics was developed by the Regional Education Laboratory for the Carolinas and Virginia (RELCV) and is designed for mathematics instruction for students in grades 1-6. The South Carolina State Department of Education has been instrumental in appraising the appropriate-ness of the program and coordinating the efforts of the South Carolina schools and the Laboratory in the pilot use of these materials.


Sign in / Sign up

Export Citation Format

Share Document