Research Studies on Learning and Teaching of Mathematics

Jinfa Cai, Gabriel J. Stylianides, Patricia Ann Kenney (eds.)

Publisher:

Springer

Publication Date:

2023

Number of Pages:

329

Format:

Hardcover

Series:

Research in Mathematics Education

Price:

119.99

ISBN:

978-3031354588

Category:

Collection

MAA Review
Table of Contents

[Reviewed by

Russell Jay Hendel

, on

02/29/2024

]

This book, dedicated to Edward A. Silver and the areas and projects benefiting from his influence, is a collection of a dozen essays on the skillful use of problem posing as an instrument to enhance mathematics instruction and learning, and should be of interest and benefit to anyone involved in mathematics education.

How teachers perceive mathematics affects how they teach it. Therefore, prior to presenting Silver’s view on what mathematics is, we present three viewpoints popular among teachers. (A) The Platonic view is that mathematics already exists in some abstract sense; mathematics is not created but discovered. (B) The instrumentalists view mathematics as a collection of already existing skills and useful procedures; the learner’s job is not creation of these skills but mastery of them allowing application to new situations. (C) The problem-solving view of mathematics believes that mathematics is constantly being created through a process of inquiry; mathematics is connected and open to revision. True mathematics focuses on the process of investigation, the connection among concepts, and the overall structure of mathematics. While the solution or correct answer may be useful it is not at the heart of mathematics.

Silver’s basic viewpoint is that problem posing is a means to learn, a means to instruct, and is a complex cognitive act which must be understood to effectively teach and learn.

With this background we can now review the other ten chapters of the book (two of which were reviewed above). The essays answer the following questions: How can the researcher assist the teacher in instruction? How and with what resources can teachers encourage mathematical problem solving? What are the features of a mathematics task that make it desirable in the sense that the task inspires inquiry, exploration, and investigation? How can we engage every student in challenging mathematical work despite classroom differentiation in ability? How can textbooks be improved to promote problem posing, inquiry, and investigation?

The book's chapters also describe projects and activities supportive to answering the above questions. 1) The QUASAR project’s goal was to provide a mathematics task framework that describes desirable mathematical task features, task levels, the evolution of mathematical instructional tasks, and how each task level affects students. 2) The professional learning tasks (PST) cycle advocates the four stages of i) Planning, ii) Enactment, iii) Debriefing, and iv) New Learning. Several researchers have commented how such cycles, allowing incremental gains, assist in the difficult task of research. 3) The book also has a chapter on family math tasks, that is, tasks, like visiting a museum, which encourage curiosity, inquiry, and investigation.

Russell Jay Hendel holds a Ph.D. in theoretical mathematics, an Associateship from the Society of Actuaries, and a Doctor of Science in Jewish Studies. He teaches at Towson University which is a center of actuarial excellence. His interests include discrete number theory, applications of technology to education, problem writing, actuarial science and the interaction between mathematics, art, and poetry.

See the publisher's website.

Tags:

Mathematics Education