In a collaborative project, two mathematics education professors, a third-grade teacher, and her students collected information from the students as they thought through how to ask, collect, and then answer their own data-driven questions. Findings indicated the students exhibited a growing understanding, sophistication, and comfort with the use…

Describes a long term teaching experiment carried out with students from grades 9 and 10. Aims at clarifying the role of the Cabri environment in teaching-learning processes. Analysis of protocols shows the possible evolution of a justification into a proof but at the same time indicates that this evolution is not expected to be simple and…

"Options". "Opinions". "Challenges". These are the key words used by a group of gifted 3rd- and 4th-grade students when asked what they want out of math. Although not surprised by the desire for challenges, most of the author's colleagues are intrigued by the students' wishes for options and opinions in math. After…

This paper has arisen as a result of teaching Models in Biology to undergraduates of Bioengineering at the Gediminas Technical University of Vilnius. The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous…

The argument examined in this paper is that music--when approached through making and responding to coherent musical structures, facilitated by multiple, intuitively accessible representations--can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students' inquiry into the bases…

Elementary education students enrolled in an experimental mathematics course participated in this study. The course is taught using a social constructivist approach and is designed to improve students' mathematical problem-solving ability and deepen their understanding of mathematics. The research question for the present study is as follows: In…

In this study we investigated relationships between convergent and divergent thinking with an emphasis on fluency, originality, flexibility and elaboration in the mathematical domain. A related purpose was to examine relationships between problem types in mathematical tasks. The math section of a performance-based assessment was used to assess 857…

As school curricula undergo changes in both content and pedagogy, pressure is placed on teacher preparation programs and undergraduate mathematics departments to model learning environments in mathematics appropriate for education students. Yet the reality of many post-secondary mathematics courses includes traditional style classes containing a…

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university.…

In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an…

This Action Research Project is meant to investigate the effects of incorporating research-based instructional strategies into instruction and their subsequent effect on student achievement in the area of problem-solving. The two specific strategies utilized are the integration of manipulatives and increased social interaction on a regular basis.…

Many K-6 teachers and students still think of mathematics as a totally separate subject from literacy. Yet incorporating math content into the language arts block helps students gain skills for reading many kinds of texts. Bringing reading, writing, and talking into the math classroom supports the development of conceptual knowledge and problem…

The new program of study for KS3 and the proposed changes in Y11 assessment for 2012 are now demanding teachers to focus again on the processes of learning. Teachers are being told they must "allow students to select the mathematics to use", "allow students to explore connected problems" and encourage them to work with real…

This study explores two approaches to directly measuring the quality of instruction: teachers' assignments with student work and focused lesson observations. The technical quality and potential feasibility of these approaches for measuring instruction in large numbers of classrooms are compared within two different content areas (reading…

Drawing from multiple theoretical frameworks representing cognitive and educational psychology, we present a writing task and scoring system for measurement of students' informative writing. Participants in this study were 72 fifth- and sixth-grade students who wrote compositions describing real-world problems and how mathematics, science, and…