In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

This study aims to establish a knowledge base on how to support students in learning. We develop an initial hypothetical learning trajectory by formulating learning activities and predicting the development of students' thinking and understanding. The methodological framework employed in this study is design research, which seeks to generate…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

This article integrated inquiry behaviors and a guided learning map (gMap) into a mobile app called Ubiquitous-Physics (U-Physics), which helps students to explore inclined plane phenomena in authentic contexts. The article investigated inquiry behaviors such as interpreting graphs, applying formulas, drawing conclusions, and peer collaboration,…

The query "When are we ever going to use this?" is easily answered when discussing the slope of a line. The pitch of a roof, the grade of a road, and stair stringers are three applications of slope that are used extensively. The concept of slope, which is introduced fairly early in the mathematics curriculum has hands-on applications…

The task shared in this article provides geometry students with opportunities to recall and use basic geometry vocabulary, extend their knowledge of area relationships, and create area formulas. It is characterized by reasoning and sense making (NCTM 2009) and the "Construct viable arguments and critique the reasoning of others"…

In this paper, we present a set of activities for an introduction to solving counting problems. These activities emerged from a teaching experiment with two university students, during which they reinvented four basic counting formulas. Here we present a three-phase set of activities: orienting counting activities; reinvention counting activities;…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

According to the National Council of Teacher of Mathematics (NCTM) (2000), K-12 students should be given an opportunity to develop their spatial reasoning abilities. One of the topics that may allow students to develop their spatial skills is forming 3-dimensional objects using spinning and extrusion methods. Also, extrusion and spinning methods…

This study offers a new method to measure navigation disorientation in web based systems which is powerful learning medium for distance and open education. The Needleman-Wunsch algorithm is used to measure disorientation in a more precise manner. The process combines theoretical and applied knowledge from two previously distinct research areas,…

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students' attempt to reach a general formula for a three-dimensional pattern generalizing task. The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate…