Investigating the Variety and Usualness of Correct Solution Procedures of Mathematical Word Problems

Abstract

The contribution focuses on issues related to the implementation of formative assessment methods into inquiry based teaching, by means of issues related to solving twelve multiple-step arithmetic word problems based on operations with natural and rational numbers. These word problems have multiple correct solution procedures and the presented qualitative exploratory empirical study investigates how varied and how usual might be correct solution procedures provided by diverse groups of solvers -future primary school teachers attending diverse university mathematics courses of diverse forms and/or time extent. According to written data collected from 149 solvers, six notions are introduced in the paper: majority, minority and even solution procedures, and majority, minority and mixed solvers. Issues regarding minority solvers are recognized as an important element for implementing formative assessment methods. All the six notions are illustrated in the paper by samples of solution procedures and diagrams of relative frequency. Implications are given for formative assessment within any kind of education involving multiple-step word problems, regardless of the extent of implemented inquiry.

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

“…This also seems to hold true in reverse, i.e., students who have a positive attitude to mathematics are more successful at solving mathematical problems [53][54][55][56][57]. The results of several authors show that success in solving mathematical problems is influenced by students' procedural skills, including their ability to use (dominantly mathematical) tools productively and to choose an appropriate representation in the mathematization of problem situations [58][59][60][61]; their level of control of processes related to mathematical activity, such as reasoning, communication, generalization, or mathematical modeling [62][63][64][65][66][67][68]; and the level of their conceptual understanding of mathematical concepts [69][70][71][72][73].…”

Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

“…The ability to solve complex open-ended problems is anchored in some various different factors including the following: (i) metacognitive knowledge [6,7], (ii) positive attitude towards mathematics [8][9][10][11][12], (iii) mastering mathematics processes as are reasoning, generalization, communicating the results or mathematical modeling [13][14][15][16][17][18] and (iv) high level of mathematical proficiency in both, procedures [19,20] and conceptual understanding [21][22][23], including arithmetic, algebraic and combinatorial thinking. These aforementioned factors are not isolated, but they rather support each other mutually in the influence of the ability to solve complex open mathematical problems [24,25].…”

Mathematical word problem solving strategy for middle school students

“…Dos de los pasos involucrados en SBI, utilizando representaciones visoespaciales y la enseñanza explícita a través de heurísticas de resolución de problemas, son de particular interés porque son exclusivos de SBI cuando se comparan con métodos igualmente complejos [7]. Jitendra, DiPipi y Perron-Jones afirman que el componente que separa al SBI de otras estrategias empíricas es el uso de diagramas.…”