In the age of the internet, it is increasingly difficult to write homework assignments in a way that encourages students to struggle with a problem on their own without seeking answers from other sources. This is especially true in lower-level courses, where students often start with the attitude of "I can't do this." In this article, I…

What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to…

The purpose of the "Identity Pole" was to explore the big idea of identity. Students would confront issues of personal and cultural meaning, and draw upon interdisciplinary connections for inspiration. The author chose to present totem poles of the Northwest Coast Native Americans/First Nations of Canada, as well as school, state and national…

Students love a mystery. So what do America's most majestic bird, a bag of habitat clues, and a soft-shelled egg have in common? This easy-to-do inquiry activity engages students as they connect clues to problem-solve how the bald eagle reached the brink of extinction in the 1960s in the lower 48 states. It was designed to give students an…

In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…

"On your mark, get set, go!" Elementary students love to hear these words as they participate in the annual Third Grade Better Boat Challenge. This highly motivational project started a few years ago as the author was developing the third-grade science curriculum to include a study that revolved around models, design, and problem solving. It has…

Students' mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students' problem-solving journals, however, do not always reflect this rather organic process. Without…

This article addresses how metacognitive skills contribute to the teaching and learning of problem solving in mathematics. It describes the development and use of a metacognitive journal activity in the classroom. (Contains 2 figures.)

Problem-based learning (PBL) works with a series of problems that form the syllabus for a course or the basis of a curriculum. Learning occurs through the definition of the problem and its attempted resolution. PBL is challenging but offers much potential for geography with its interdisciplinary character. The challenge to geography lecturers is…

Describes the use of math journals in one kindergarten classroom. Asserts that use of the journals, in which children record their problem-solving processes, makes them think about and use various symbols to represent their thoughts; keeps them actively involved in reasoning, comparing, counting, and other mathematical concepts; and encourages…

Students are rarely given the opportunity of being decisionmakers in class, and when they are, they may feel unsure of how to organize their own learning. However, over time they come to appreciate the benefits of a more active engagement in learning English. In this paper, I describe a procedure based on Exploratory Practice (EP) for guiding…

Explains task definition which is the first stage in the Big 6, an approach to information and technology skills instruction. Highlights include defining the problem; identifying the information requirements of the problem; transferability from curriculum-based problems to everyday tasks; and task definition logs kept by students. (LRW)

Undergraduate science students took an Inquiry course in their second (sophomore) year. The course was designed to explore the social life of scientific knowledge. They were given a set of eight assessment options: personal logs, targeted oral examinations, commentaries, mini-lectures, individual explorations, research proposals, book reviews, and…

Describes use of focused prompts with student journals in a college mathematics course at Ohio State University. Students were asked to complete two writing tasks weekly to describe what they had learned from specific topics, and work out one problem in detail, with explanatory notes describing errors and false starts. Students' attitude toward…

In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…