Children's learning of early number bonds is a significant issue in South African schools because evidence shows that flexible and efficient (fluent and reasoned) knowledge of number bonds to 20 correlates with success at the end of primary schooling, yet the evidence is that many South African students are over-reliant on inefficient counting…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

Children learn arithmetic procedures by rote, rather than by constructing them with an understanding of numbers. Rote learning produces lack of flexibility, nonsensical errors, and other difficulties. Proposed is a theory of conceptual understanding and its role in learning and executing arithmetic procedures. The basic hypothesis is that…

This document presents information on open learning environments in Adult Basic Education in The Netherlands. It focuses on the role of teacher, tutorial, progress, and evaluation methods. Several task groups address the four dimensions in a learning environment: accommodation, time, infrastructural, and social psychological. Through independent…

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

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)

This study investigated the effectiveness of finger mathematics with elementary pupils in second grade. The sample consisted of 56 pupils located in a lower socioeconomic area of Chicago. Half the pupils were taught using the finger method; the other half experienced the traditional textbook paper-and-pencil method. The results indicated that…

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)

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)

A first grade teacher in a rural elementary school in upper East Tennessee observed that her students needed a better way to improve their computation skills than those of traditional instructional methods. The school system's new Mathematics textbook was correlated with commercial Mathematics software. The teacher wanted to find out if using this…

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)