Development of Teaching Materials Algebraic Equation to Improve Problem Solving

Problem-solving skills are the basic capabilities of a person in solving a problem and that involve critical thinking, logical, and systematic. To solve a problem one-way necessary measures to solve the problem. Polya is one way to solve a mathematical problem. by developing teaching materials designed using the steps in solving problems Polya expected students could improve its ability to solve problems. In this first year, the goal of this study is to investigate the process of learning the hypothetical development of teaching materials. This study is a research & development. Procedure development research refers to research the development of Thiagarajan, Semmel & Semmel ie 4-D. Model development in the first year is define, design, and development. The collection of data for the assessment of teaching materials algebra equations conducted by the expert by filling the validation sheet. Having examined the materials of algebraic equations in the subject of numerical methods, reviewing the curriculum that is aligned with KKNI, and formulates learning outcomes that formed the conceptual teaching material on the material algebraic equations. From the results of expert assessment team found that the average ratings of teaching materials in general algebraic equation of 4.38 with a very good category. The limited test needs to be done to see effectiveness teaching materials on problem-solving skills in students who are taking courses numerical method

Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction

A Global Approach for Solving Edge-Matching Puzzles

We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this problem and provide conditions under which it exactly characterizes a puzzle. Using the new representation, we recast the combinatorial, discrete problem of solving puzzles as a global, polynomial system of equations with continuous variables. We further propose new algorithms for generating approximate solutions to the continuous problem by solving a sequence of convex relaxations

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces

Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attampts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction