Addition and subtraction of three-digit numbers: adaptive strategy use and the influence of instruction in German third grade

Empirical findings show that many students do not achieve the level of a flexible and adaptive use of arithmetic computation strategies during the primary school years. Accordingly, educators suggest a reform-based instruction to improve students’ learning opportunities. In a study with 245 German third graders learning by textbooks with different instructional approaches, we investigate accuracy and adaptivity of students’ strategy use when adding and subtracting three-digit numbers. The findings indicate that students often choose efficient strategies provided they know any appropriate strategies for a given problem. The proportion of appropriate and efficient strategies students use differs with respect to the instructional approach of their textbooks. Learning with an investigative approach, more students use appropriate strategies, whereas children following a problem-solving approach show a higher competence in adaptive strategy choice. Based on these results, we hypothesize that different instructional approaches have different advantages and disadvantages regarding the teaching and learning of adaptive strategy use.

[1]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[2]  Susan B. Empson,et al.  A longitudinal study of invention and understanding in children's multidigit addition and subtraction , 1998 .

[3]  R. Siegler,et al.  Four aspects of strategic change: Contributions to children's learning of multiplication. , 1995 .

[4]  A. W. Blöte,et al.  Students' flexibility in solving two-digit addition and subtraction problems : Instruction effects , 2001 .

[5]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[6]  Lieven Verschaffel,et al.  The Development of Children's Adaptive Expertise in the Number Domain 20 to 100 , 2006 .

[7]  Sybille Schütte,et al.  Rechenwegnotation und Zahlenblick als Vehikel des Auf baus flexibler Rechenkompetenzen , 2004 .

[8]  Andrew C. Porter,et al.  Do Textbooks Dictate the Content of Mathematics Instruction in Elementary Schools? , 1989 .

[9]  Lieven Verschaffel,et al.  Whole number concepts and operations , 2007 .

[10]  Ian Thompson,et al.  Issues in Teaching Numeracy in Primary Schools , 1999 .

[11]  A. W. Blöte,et al.  Mental computation and conceptual understanding , 2000 .

[12]  T. P. Carpenter,et al.  Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction. , 1997 .

[13]  Ann Dowker,et al.  The Development of Arithmetic Concepts and Skills , 2003 .

[14]  James Hiebert,et al.  Instruction, Understanding, and Skill in Multidigit Addition and Subtraction , 1996 .

[15]  Karen C. Fuson,et al.  Research on whole number addition and subtraction. , 1992 .

[16]  Ann Dowker,et al.  The development of arithmetic concepts and skills: Constructing adaptive expertise , 2003 .

[17]  Christoph Selter,et al.  Addition and Subtraction of Three-digit Numbers: German Elementary Children's Success, Methods and Strategies , 2001 .

[18]  L. Verschaffel,et al.  Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education , 2009 .

[19]  Lieven Verschaffel,et al.  Acquisition and use of shortcut strategies by traditionally schooled children , 2009 .

[20]  C. Benz,et al.  Die Entwicklung der Rechenstrategien bei Aufgaben des Typs ZE±ZE im Verlauf des zweiten Schuljahres , 2007 .

[21]  John Threlfall,et al.  Flexible Mental Calculation , 2002 .

[22]  Ian Thompson,et al.  Mental Calculation Strategies for Addition and Subtraction , 1999 .

[23]  Elisabeth Rathgeb-Schnierer,et al.  Kinder auf dem Weg zum flexiblen Rechnen: Eine Untersuchung zur Entwicklung von Rechenwegen bei Grundschulkindern auf der Grundlage offener Lernangebote und eigenständiger Lösungsansätze , 2007 .

[24]  Monica Johansson,et al.  Textbooks in mathematics education : a study of textbooks as the potentially implemented curriculum , 2003 .

[25]  A. Treffers,et al.  The empty number line in Dutch second grades: Realistic versus gradual program design , 1998 .

[26]  Lieven Verschaffel,et al.  Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction , 2009 .

[27]  Mike Askew,et al.  Principles and Practices in Arithmetic Teaching , 2001 .

[28]  Didaktik der Mathematik Beiträge zum Mathematikunterricht , 1988 .

[29]  Meindert Beishuizen,et al.  Mental Strategies and Materials or Models for Addition and Subtraction Up to 100 in Dutch Second Grades. , 1993 .