Is it true, as many assert, that common fractions will become obsolete?
Zalman P. Usiskin
Zalman P. Usiskin
Materials were written for an entire year's course in geometry in which transformations were used to develop the concepts of congruence, similarity, and symmetry, as well as being a vehicle for proof. This paper presents a study involving 413 students using these materials and 483 control students, comparing performance on standard geometry content and attitudes. Preliminary studies were done on perceptual, arithmetic, and algebraic skills. Student comprehension of transformation-related concepts, the problem of implementation, and attitudes of teachers were informally studied. While the data indicated that the experimental Ss could learn the material, few differences were detected with the measures employed--a significant difference (p<.01) in favor of the C group was found on the posttest of standard geometry content. Pre-(September) and posttest (June) student attitude data indicated a change in mean score, less positive, for both E and C groups (p<.01 for the C group). Attitude differences between E and C were not significant. Informal feedback from a teacher questionnaire indicated a favorable reaction to the experimental materials.
From the 1980s: What Should Not Be in the Algebra and Geometry Curricula of Average College-Bound Students?
A strong argument is presented. Does it reflect your thinking?
In this September 1980 article the author argues that curriculum is overcrowded and some topics should be deleted or replaced by more modern ones. He proposes for deletion several topics from algebra and geometry based on pragmatic criteria of whether the topic has real life application clearly understood by student and whether it is used in later courses. The author suggests removing word problems from algebra and some proof from geometry asserting among other that “A computer program is much like a proof”.
Reconsidering the 1980s: What Should Not Be in the Algebra and Geometry Curricula of Average College-Bound Students?
A Retrospective after a Quarter Century
This article gives a retrospective view on major changes in mathematics education the last 25 years. It notes increased enrollment in higher mathematics courses, earlier grade levels at which algebra and geometry are taken, multiplicity of standards and assessments. The author looks back on his recommendation given in 1980 and presents his assessment of their validity under current conditions.
Zalman Usiskin and Sharon Senk
Test instruments are an important element of almost every study in mathematics education, and the test that is used obviously affects the results of the study. Yet often a test is assumed both valid and reliable, and neither its content nor its psychometric properties are given scrutiny. The analyses Crowley and Wilson have done with the Van Hiele Geometry Test are welcome.
Elizabeth Fennema and Zalman Usiskin
Zalman Usiskin and Max S. Bell
When we speak of applications of rational numbers, we refer to those applications that involve more than just whole numbers or integers. Most textbooks outline such applications.
Zalman P. Usiskin and Arthur F. Coxford
There are many individuals who have called for the insertion of transformations into the tenth-grade geometry course; for example, Jeger (1966, preface), Adler (1968, p. 226), and Betz (1933, p. 110). For some time, texts have been appearing with a section or chapter devoted to reflections, rotations, or other kinds of transformation (Kelly and Ladd 1965; Fischer and Hayden 1965; Fehr and Carnahan 1961; and Jurgensen; Donnelly; and Dolciani 1969).
Daniel B. Hirschhorn, Denisse R. Thompson, Zalman Usiskin and Sharon L. Senk
The University of Chicago School Mathematics Project (UCSMP) was begun in 1983 as an attempt to implement the recommendations of many reports to improve school mathematics. The national reports available at the time (e.g., NACOME [1975); NCTM ; CBMS [19821; College Board [19831; NCEE [1983)) called for a curriculum of broader scope that would include statistics, probability, and discrete mathematics and that would give strong attention to applications, use the latest in technology, and emphasize problem solving. To accomplish the curricular revolution recommended by these reports, it was essential that new, appropriate materials be written. History had shown that neither materials written for the best students, such as those from the new-math era, nor materials written for the slower students, such as those popular in the backto-basics movement, were appropriate for the vast majority of students without major revisions (Usiskin 1985). Thus UCSMP started with the goal of developing mathematics for all grades K–12 that would be appropriate for the majority of students in the middle.
Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer, Alan Schoenfeld, Cathy Seeley, Dan Teague and Zalman Usiskin
Countries that have made progress on international assessments of mathematics achievement have national consensus on goals and sustained commitment to change over time. The Common Core State Standards provide a framework for such effort in the U. S., if we focus on five key elements of curriculum, teaching, and assessment.