The Learning Trajectory Construction of Elementary School Students in Solving Integer Word Problems

Accepted: 05.07.2021 The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories in solving integer word problems. The aim of this study is to produce a learning trajectory that can be used to solve integer word problems using traditional games. This study used a design-based research. Participants in this study were five grade sixth elementary school students. There are 6 sub-topics studied, i.e., the concept of negative integers, sequence integers, addition and subtraction operations, division and multiplication operations, mixed count operations, and solving problems related to integers. The results of this study obtained student learning trajectories for each sub-topic including the free play, collecting data from the game results, making mathematical relationships, building concepts, and applying them to various problems. Students are able to do problem-solving based on the sequence of tasks but require intervention so they can apply it to other situations without engaging in activities. Further research is required for more in-depth exploration on thinking process, instruction types, and behaviours that students might display independently without using traditional games in solving integer word problems.

[1]  I. Elia.  Word problem solving and pictorial representations: insights from an exploratory study in kindergarten , 2020 .

[2]  Michelle Stephan,et al.  A Proposed Instructional Theory for Integer Addition and Subtraction , 2012 .

[3]  A. O. Pfnister.  Toward a Theory of Teaching , 1963 .

[4]  Martin A. Simon.  An emerging methodology for studying mathematics concept learning and instructional design , 2018, The Journal of Mathematical Behavior.

[5]  Susanne Prediger,et al.  Enhancing Fifth Graders’ Awareness of Syntactic Features in Mathematical Word Problems: A Design Research Study on the Variation Principle , 2020 .

[6]  Julie Sarama,et al.  Mathematics Learned by Young Children in an Intervention Based on Learning Trajectories: A Large-Scale Cluster Randomized Trial , 2011 .

[7]  Kpe Koeno Gravemeijer.  Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education , 2004 .

[8]  Martin A. Simon,et al.  Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development. , 2016 .

[9]  Sri Adi Widodo,et al.  Single subject research: use of interactive video in children with developmental disabilities with dyscalculia to introduce natural numbers , 2021, Participatory Educational Research.

[10]  Ufuk Özkubat,et al.  Mathematical Problem-Solving Processes of Students with Special Needs: A Cognitive Strategy Instruction Model Solve It , 2020 .

[11]  Shu Zhang,et al.  Characteristics of teaching and learning single-digit whole number multiplication in china: the case of the nine-times table , 2019, ZDM.

[12]  Y. Xin.  The effect of a conceptual model-based approach on ‘additive’ word problem solving of elementary students struggling in mathematics , 2018, ZDM.

[13]  C. Drake,et al.  Examining aspects of teachers’ posing of problems in response to children’s mathematical thinking , 2018, Journal of Mathematics Teacher Education.

[14]  Christopher R. Rakes,et al.  Rethinking Mathematics Misconceptions: Using Knowledge Structures to Explain Systematic Errors within and across Content Domains , 2018 .

[15]  K. Akyeampong,et al.  Trapped in low performance? Tracking the learning trajectory of disadvantaged girls and boys in the Complementary Basic Education programme in Ghana , 2020, International Journal of Educational Research.

[16]  G. Harel,et al.  An operational definition of learning , 2010 .

[17]  Roger Howe.  Learning and using our base ten place value number system: theoretical perspectives and twenty-first century uses , 2019 .

[18]  Masami Isoda,et al.  Lesson Study: Problem Solving Approaches in Mathematics Education as a Japanese Experience , 2010 .

[19]  D. Clements,et al.  Learning and Teaching Early Math: The Learning Trajectories Approach , 2009 .

[20]  Craig J. Cullen,et al.  Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3: A Longitudinal Study , 2012 .

[21]  Jere Confrey,et al.  Design research with a focus on learning processes: an overview on achievements and challenges , 2015 .

[22]  Eric Weber,et al.  Expanding Notions of “Learning Trajectories” in Mathematics Education , 2015 .

[23]  Nicole L. Fonger,et al.  A quadratic growth learning trajectory , 2020 .

[24]  C. Csíkos,et al.  Teachers’ pedagogical content knowledge in teaching word problem solving strategies , 2019, ZDM.

[25]  Amy B. Ellis,et al.  An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation , 2016 .

[26]  Bridging whole numbers and fractions: problem variations in Chinese mathematics textbook examples , 2018, ZDM.

[27]  Eric Weber,et al.  The duality between ways of thinking and ways of understanding: Implications for learning trajectories in mathematics education , 2014 .

[28]  L. Verschaffel,et al.  Word problems in mathematics education: a survey , 2020 .