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.
Highlights
One of the educational concerns that has attracted quite a lot of attention across countries in recent decades relates to looking for sustainable ways of implementing inquiry based education into everyday teaching and learning of various school subjects at various school levels
The diagrams have been composed as follows: the sectors related to incorrect solution procedures are shaded, the sectors related to correct solution procedures are unshaded, the labels that are written in italics belong to word problems with different correct solution procedures evenly used by the solvers, the labels in bold roman belong to word problems with majority and minority correct solution procedures
The sectors related to incorrect solution procedures are shaded in the diagrams, the sectors related to correct solution procedures are unshaded, the labels written in italics belong to word problems with evenly used correct solution procedures and the labels in bold roman belong to word problems with majority and minority correct solution procedures
Summary
One of the educational concerns that has attracted quite a lot of attention across countries in recent decades relates to looking for sustainable ways of implementing inquiry based education into everyday teaching and learning of various school subjects at various school levels. Data analysis from that contribution was enriched by additional data from three other groups of participants that all attended university mathematics courses on the same mathematical content as the original group of participants but their courses differed in the form of teaching and/or time extent Such an enrichment offered a wider variety of outcomes and the method of constant comparison led to more precise specifications of notions related to usualness of correct solution procedures that had been newly established in (Samková, 2019) as well as to the establishment of another new notion. The text is organized as follows: at the beginning, it presents the context of the study (inquiry based mathematics education, word problems with multiple solution procedures and formative assessment), the four groups of participants and the diagnostic instrument It describes consecutively the four stages of the study (the course of data collection and data analysis, findings, emerging concerns), discusses their findings and captures further implications for our research project
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