The use of a type of magic square as a tool for student drill in the basic operations is emphasized. Methods for constructing "Sneaky Squares" are outlined and the logic behind them explained. The approach is seen as convenient for a variety of basic drill work. (MP)

These materials were developed in response to the Utah State Board of Education's new high school graduation requirements, particularly as they relate to the identification, teaching, and assessment of certain basic functional competencies. The document has been compiled as a guide and aid to mathematics teachers. Thirty competencies have been…

This critique discusses Gagne's position that students should understand how to mathematize a concrete situation and validate a solution but need not understand how a solution is derived. Reconciling his views with those of mathematics educators and raising questions are both included. (MNS)

Gagne's reply to critiques by Wachsmuth and by Steffe and Blake notes that their approaches are from different points of view. He urges that mathematics educators examine critically the view that understanding involves some aspects of the structure of mathematics. (MNS)

A way to cast computational practice or review in a problem-solving context without moving into word problems is presented. The game described is viewed as an instructional tool that will allow pupils to explore and help them to develop forerunners of important mathematical problem-solving skills. (MP)

A brief history of computers, a description of uses, and a disucssion of various types available are all given. Specific examples where the computer may be used to help teach mathematics are presented with some sample programs explained. A selected annotated bibliography is included. (LS)

This critique focuses on Gagne's attempt to apply information-processing theory to mathematics education, noting that this distorts what it means to learn mathematics. This is discussed with specific illustrations. (MNS)

It is noted that defining subtraction independently of addition through use of physical objects can help one to illustrate the non-commutativity of this operation. Lack of awareness of the importance of the order of the digits may be a primary cause of errors in compound subtraction. (MP)

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

Pupil difficulty with understanding mathematical sentences is viewed as a problem with reading comprehension. Suggestions are made for ways to help children over the "missing-addend hurdle." The focus is on an educational game that has been used successfully to get students to focus on the meaning of mathematical sentences. (MP)

An overview is provided of the current literature on mathematical learning of children with a learning disability. Mathematics for the population viewed is seen to mean mainly arithmetic. It is felt more research is clearly needed on teaching arithmetic to children with a learning disability. (MP)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

The material is designed for pupil practice in: (1) associating numerals with sets of objects and finding sums of two or three numbers; (2) subtracting, one- and two-digit numbers with some regrouping; (3) mental computation using the basic operations; and (4) using combinations of basic operations with whole numbers and decimals. (MP)