We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

Escape rooms have been receiving more attention for use in education. Escape rooms are games in which teams solve multiple puzzles and challenges using clues, hints, and strategy to determine how to escape from a locked room. The implementation of escape rooms has the potential for increasing students' mathematical understanding and engagement.…

This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or…

Suggests using episodes from the history of mathematics as source material for mathematical investigations, particularly for use in teaching problem solving. Representative examples are included. (JN)

Introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. Describes components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies. (Author/MM)

The National Science Education Standards (NSES; National Research Council [NRC], 1996) include Science and Technology as one of the eight categories of content standards. The science and technology standards establish connections between the natural and designed worlds and provide students with opportunities to develop decision-making abilities.…

Compares the ability of students in Michigan (N=302) and Scotland (N=221) to do simple calculation exercises and relational/practical problems involving number and operation. Although this is not a controlled statistical study (data collected included birth date and sex), sample sizes are sufficient to make the reported results meaningful. (JN)

Describes an NCTM Standards-based high school mathematics curriculum that involves application, technology, cooperative learning, and open-ended problem solving and compares student attitudes and achievement with a traditional class. Results indicate significant attitude improvement in the mathematical confidence of students in the experimental…

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit…

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

Described is science education's role in the back to the basics movement. Science education is described as providing opportunities for the development of (1) logical structures, (2) the understanding of the scientific processes, and (3) the development of creative problem solving techniques. (Author/DS)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)