When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Mathematical and computational thinking (CT) are closely interrelated, yet CT integration into mathematics instruction remains limited. This study aims to analyze the effectiveness of the teaching process for straight-line equations in enhancing students' CT skills and to propose improvements based on the findings. A qualitative case study…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined 1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction and 2)…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction; and…

This paper demonstrates how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. We examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance prediction; and (2) what types of in-game features were associated with student…

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

The aim of this article is to identify the natural relationships that exist between using computer programming in BASIC, and some particular mathematical concepts. Specific examples are given for use by the mathematics teacher who has the necessary facilities available. (MN)

The author proposes that computer programs which are designed to make algorithmic structures accessible and comprehensible be employed as advance organizers in mathematics instruction. These programs would bring clarity and structural integration to mathematical, instructional, and cognitive structures important to the mastery of mathematical…

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

A teaching sequence for the division algorithm is detailed. (MP)