Strategies for Basic-Facts Instruction

Abstract

In a class of beginning second graders, children explained with these typical replies how they solved the number fact 8 + 7: “I know 7 + 7 is 14, and 1 more is 15”; “8 + 2 makes 10. But 7 has 5 more, so the answer is 15”; and “I just knew the answer was 15.” Teaching basic number facts like 8 + 7 has been a goal of elementary mathematics instruction for more than 100 years and continues to be important today.

A Comparative Analysis of Number Sense Instruction in Reform-Based and Traditional Mathematics Textbooks

“…Although many educators recognize that the quality and adequacy of mathematics textbooks are important factors in promoting student learning, few content analyses have focused on the implications of instructional design for learners at risk for mathematics disabilities (Carnine, Jitendra, & Silbert, 1997;Jitendra, Carnine, & Silbert, 1996;Jitendra, Griffin, et al, 2005;Jitendra, Salmento, & Haydt, 1999). None of these studies, however, have compared instruction presented in reformbased and traditional textbooks or have focused on beginning mathematics skills such as number sense, which is a prerequisite for the development of higher-level mathematics skills (Isaacs & Carroll, 1999;Markovits & Sowder, 1994;McIntosh, Reys, & Reys, 1992;NCTM, 1989NCTM, , 2000NRC, 1989). The purpose of our study was to compare how number sense was taught in reform-based and traditional mathematics textbooks.…”

The Differential Effects of Teaching Addition Through Strategy Instruction Versus Drill and Practice to Students With and Without Learning Disabilities

“…At present, it is generally accepted that even if students are not automatic with basic facts, they should be engaged in activities that promote the development of number sense and mathematical reasoning (Gersten & Chard, 1999); still, much time and energy are spent in classrooms trying to achieve automaticity in basic arithmetic facts. The argument guiding such efforts is that automaticity is useful both in and out of the classroom (Isaacs & Carroll, 1999). Typically, students are taught how to become automatic either through the provision of drill and practice or through the direct teaching of a strategy.…”

“…Eventually, basic arithmetic facts should become declarative knowledge, which can be conceptualized as an interrelated network of relationships containing problems and their answers. Researchers have maintained that teaching children different strategies can help the learning and retention not only of higher order concepts and problems, but even of the basic addition facts (e.g., Isaacs & Carroll, 1999;Steinberg, 1985).…”

Αλγοριθμικές Διαδικασίες Ως Κύρια Μαθηματική Γνώση

“…Όλοι, σχεδόν, συμφωνούν για τη σπουδαιότητα της αβίαστης ανάκλησης των αριθμητικών δεδομένων, αλλά υπάρχουν διχογνωμίες και ασάφειες για τον τρόπο που θα επιτευχτεί αυτή (Isaacs & Carroll, 1999). Γενικά, δύο είναι οι διδακτικές προσεγγίσεις, οι οποίες στοχεύουν στην αυτοματοποίηση των δεδομένων.…”

“…Ο Strother (2010) και οι Isaacs & Carroll (1999) προτείνουν για τα δεδομένα της πρόσθεσης δυο στρατηγικές: α) τις παραλλαγές με βάση την πρόσθεση διδύμων (π.χ. 7+8 = 7+7+1 = 8+8-1 = 15 ή 6+8 = 6+6+2 = 12+2 = 8+8-2 = 14) και β) τη δημιουργία στρατηγικών, για κάθε δεδομένο, με βάση το 10 (π.χ.…”