Digital technologies have the potential to revolutionize education by enhancing quality, fairness, and efficiency. However, equitable access to these technologies remains a challenge. ILSAs (international large-scale assessments) have shown that the relationship between digital use and performance varies across countries and over time. To fully…

In 2010, the William and Flora Hewlett Foundation's Education Program has established the Deeper Learning Initiative, which focuses on students' development of deeper learning skills (i.e., the mastery of core academic content, critical-thinking, problem-solving, collaboration, communication, and "learn-how-to-learn" skills). Two test…

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Provides guidelines for developing and implementing lessons using selections from children's literature as meaningful and appropriate contexts for solving word problems. Selection procedures, materials for constructing the characters, and two sample problems are provided. Lists 15 references. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

Dyscalculia is considered to be a learning difficulty or difference. It is increasingly being recognised and "diagnosed" within adult learning. However, practitioners are often unclear about whether learners who are considered to have dyscalculia are entitled to access arrangements for examinations and assessments, and which access…

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

In this project, a plan for solving word problems based on the students' level of development was developed. A 10-week implementation of a plan for solving word problems at the concrete level of development included the use of a flow chart or plan to map out and solve word problems. Students then used the flow chart and manipulatives to develop…

This report attempts to discover how students think about and use mathematics in open-ended questions. Part I, "Open-ended Questions in Mathematics," describes the rationale for adding open-ended questions to the grade 12 mathematics test of the California Assessment Program (CAP). Part II describes the findings from students' responses…

This document contains overviews of current research, insights from teachers and tutors, and considerations of such issues as metacognition, choice of operations, and the testing of problem-solving skills. Papers include: (1) "Historical Perspectives on Problem Solving in the Mathematics Curriculum" (George M. A. Stanic and Jeremy…

This report describes a computer-based instructional system, the Story Problem Solver (SPS). SPS provides students with instruction about the semantic structure of story problems. It was developed to test a specific schema theory of knowledge organization in long-term memory. For this reason SPS depends explicitly upon a theory of the relationship…

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

This manual describes the Mathematics Assessment Questionnaire (MAQ) and its development, provides relevant background from the research literature, describes approaches to the reporting and uses of the MAQ (including its use in instructional planning), and presents sample responses from students and classes. The MAQ provides teachers and students…