Mastering by the teacher of the instrumental genesis in CAS environments: necessity of instrumental

In this article, we study didactic phenomena identified in integration experiments within our classes, CAS(implemented in calculators). From this study, we show the interest of an instrumental approach to understand the influence of tools on the mathematical approach and on the building of students' knowledge: through a process - instrumental genesis - a calculator becomes a mathematical work tool; this process depends on the tool's constraints and potentialities, on students' knowledge, and on

Design of adaptive feedback in a web educational system

This paper presents our interdisciplinary approach for the design of a technology-based learning environment for orthopaedic surgery. We present how we designed a part of this environment. This part is in relation to the web environment. The key idea is to produce an intelligent feedback in relation to the learner's activity. The didactical analysis of teaching and learning in the workplace gives a framework to build the computational representation of knowledge. This analysis is shown within th

PBL Especially in the Context of Large Classes

This webpage from McMaster University in Canada describes one approach using small groups for using problem-based learning in teaching large classes. The focus of the authors is on teaching medical students but they also describe use of this approach in teaching civil engineering students, geography, etc. The approach described is likely to be of interest to analytical chemistry faculty teaching large classes of undergraduates as well. Links near the end of the document to pdf files contain u

Middle School Portal: Math and Science Pathways (MSP2)

This is one of the best online resources about fractals, and is meant to support a first course in fractal geometry for students without especially strong mathematical preparation. The site is incredibly deep, providing everything from the most basic definitions and non-technical discussions to involved mathematical formulations. Interactive Java applets, downloadable software for the PC and Macintosh, and laboratory activities are also presented. A particularly interesting section of the site e

GoMath

Grade school students will find GoMath.com a valuable online tutor for almost any topic in mathematics. The three most useful sections of the site are Algebra Solutions, Geometry Solutions, and Formula-To-Go. The first two explain many common mathematical properties and offer mini-lessons and worksheets about each topic. Formula-To-Go has equations, tables, and calculus identities that make an excellent quick reference. Another section that is better suited for practice is the questions archive.

Middle School Portal: Math and Science Pathways (MSP2)

Using this online activity, students explore the meaning of probability using the pigeonhole principle. The initial question asks students to determine the probability that someone who is not paying attention to what she is doing can put checks into the correct envelopes. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution hint suggests experimenting with the possible outcomes with checks a, b,

Middle School Portal: Math and Science Pathways (MSP2)

In this activity, students use hits and at-bat data to determine which of two baseball players has a better batting average. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity contains a solution hint, a complete explanation of the answer that reveals the surprising answer, and additional problems related to finding averages. Information about baseball averages and fractions is included. Copyr

Math Teaser

Every month we will give you a math/statistics brain teaser that lets you test your knowledge with a fun problem.Many of the ideas in these Teasers come from thoughts formed by some of the great mathematical/statistical geniuses in history.

Supporting a Learner Community with Software Agents

This paper describes a multi- agent approach that aims at supporting learners involved in a collective activity. We consider pedagogical situations where students have to explicitly define the articulation of their collective work and then achieve the different tasks they have defined. Our objective is to support these students by taking some of these tasks in charge whilst making them work out such organisation features. For this purpose, we propose to consider that the group of students forms

The Development and Use of Representations in Teaching and Learning about Problem Solving: Exploring

Tim Boerst has explored instructional approaches that foster the development of representational skill and routine use of multiple representations in problem solving. In particular he has used the 'Rule of 3' (a structure employed in calculus reform materials that highlights the use of numerical, algebraic, and/or graphic representations in mathematical learning) to see whether an emphasis on multiple representations would deepen mathematical learning opportunities for a wide variety of students

A primer in MathML

This course, as the name suggest, is intended to help authors who want to publish mathematical content on web. The emphasis here is to enable learners to quickly adapt to the extensive mathML markup language and begin writing codes even without a specialized editor, available commercially. The course is presented in the form of a tutorial, which essentially saves on unnecessary details. This tutorial is not intended currently (may be supplemented later with the help coming from others) to be a c

Mathematics for Computer Science

A basic introduction to Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive calcu

Patrons d'exercices pour Aplusix Une étape du développement de l'EIAH occasion d'un travail entre

Au cours du développement de l'EIAH APLUSIX, il y a eu de nombreuses occasions d'un travail partagé entre informaticiens et didacticiens. Quelques-unes sont décrites succinctement. Lors de la mise en place de patrons d'exercices et d'une carte de tests, une coopération plus approfondie a eu lieu, en respectant les disciplines de chacun. Cette mise en place de patrons d'exercices est décrite plus longuement.,Preprint

Empirical Research Methods

Regression analysis is an enormously popular and powerful tool, used ubiquitously in the social and behavioral sciences. Most courses on the subject immediately dive into the mathematical aspects of the subject and illustrate the technique on problems that are already highly structured. As a result, most students come away with little idea of the wide range of problems to which regression analysis can be applied and how to represent those problems in a way that cleverly utilizes readily availabl

Logic

Logic and Proofs is an introduction to modern symbolic logic. It provides a rigorous presentation of the syntax and semantics of sentential and predicate logic. However, the distinctive emphasis is on strategic argumentation. Students learn effective strategies for constructing natural deduction proofs. This learning is supported by the Carnegie Proof Lab: it provides a sophisticated interface, in which students can give arguments by strategically guided forward and backward steps.

Private Universe Project in Mathematics: Workshop 3. Inventing Notations

We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,Kenilworth Study: Pizzas In the fourth grade, the students encounter counting problems where the solutions cannot be built using standard manipulatives. As he invents his own notation systems, one student, Matt, builds on previous work to arrive at a solution

Private Universe Project in Mathematics: Workshop 2. Are You Convinced?

Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,25 min. Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part

Private Universe Project in Mathematics: Workshop 2. Are You Convinced?

Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to give

Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician

What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the childrens game Towers of Hanoi, she explains her approach to solving problems. 15 m

Chemical Equilibrium in the Gas Phase

This website describes gas phase equilibrium chemistry and provides a tutorial on key concepts like LeChatelier's principal and includes on-line exercises in which the reader can check their understanding. Calculations of equilibrium constants expressed in terms of pressure and concentration are presented. This site will be most useful for high school and introductory university Chemistry courses in which students are developing an understanding of equilibrium chemistry.