In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

Cignition delivers virtual tutoring in math and ELA, led by experienced educators. Their approach focuses on data-informed instruction and collaborative learning that encourages student-to-student interaction to build students' conceptual understanding. After a 2020 efficacy study of its 1:1 math tutoring offering, Cignition developed a group…

Authoring tools for Intelligent Tutoring System (ITS) have been shown to decrease the amount of time that it takes to develop an ITS. However, most of these tools currently do not extend to collaborative ITSs. In this paper, we illustrate an extension to the Cognitive Tutor Authoring Tools (CTAT) to allow for development of collaborative ITSs that…

Collaborative and individual learning are both frequently used in classrooms to support learning. However, little research has investigated the benefits of combining individual and collaborative learning, as compared to learning only individually or only collaboratively. With our study, we address this research gap. We compared a combined…

While collaborative Intelligent Tutoring Systems (ITSs) have been designed for older students and have been shown to support sense-making behaviors, there has not been as much work on creating systems to support collaboration between elementary school students. We have developed and tested, with 84 students, individual and collaborative versions…

A 6-day (April 11th to 16th, 2011) experimental study as a part of Continuous Professional Development was launched at three districts i.e. Dadu, Naushahro Feroz, Mirpurkhas to enable public sector primary school teachers (PSTs) to translate the abstract concepts of fractions (grade 2 to 5) into concrete learning using low or no cost available…

Describes three classroom techniques involving bulletin boards for the mathematics classroom; a visual representation of fractions in which the school day is broken up into parts by hour; and methods to test and review mathematical concepts while students work cooperatively. (MDH)

Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Describes the "number 2 arithmetic challenge," an activity in which students score points by creating examples using the number 2 that satisfy an unknown rule. Computers are utilized to verify and record examples. Conflicts with computer responses create situations to explore negative numbers, fractions, mixed numbers, the order of…