Mathematics

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools.

Instructional principles gleaned from cognitive science play a critical role in improving classroom teaching. This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S. Based on the analysis of 32 videotaped lessons of inverse relations, we found that most teachers spent sufficient class time on worked examples; however, some lessons included repetitive examples that also included irrelevant practice problems.

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS).

This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks. Student work was documented through the use of smartpen technology which allowed the researchers to "track" students' written work on the proof tasks as well as hear the students' explanations of their thinking about the tasks. Although the two tasks highlighted in this paper were relatively routine triangle congruent proofs, only 7 out of 23 of the sampled students were successful on both proofs.

Beyond initial college preparation, secondary teachers in the United States have few professional opportunities to do and learn challenging mathematics, especially incollaboration with colleagues. The Mathematics Immersion for Secondary Teachers at Scale program engages sets of teachers in local school sites, connected synchronously and asynchronously to colleagues in other sites, in doing mathematics designed to promote experiences of mathematical immersion, community, and connection to the work of teaching.

In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional triangle as a means to coordinate them to illustrate the observable relationships among teacher, students(s), and content.

In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional triangle as a means to coordinate them to illustrate the observable relationships among teacher, students(s), and content.