Using Number Line Procedures and Peer Tutoring to Improve the Mathematics Computation of Low‐performing First Graders

Abstract

Recommendations for mathematics instruction frequently include the use of manipulatives as a critical component. There are few experimental analyses of teaching strategies involving the use of manipulatives (e.g., the number line). This investigation used a multiple baseline design across three groups of students to examine the effectiveness of an experimental procedure for improving low‐performing children's skills in solving missing addend arithmetic problems using the number line. To address concerns about inadequate time for instruction and insufficient practice in most mathematics instruction, trained peer tutors implemented the procedure. The results suggest that student performance improved when trained tutors taught the students number line procedures and gave them feedback on accuracy. Further, social validation data indicate that the students, their tutors, and their classroom teachers liked the procedures.

Are diagrams always helpful tools? Developmental and individual differences in the effect of presentation format on student problem solving

“…Can instruction improve students’ ability to use the diagrams when solving algebraic story problems? Research in both mathematics education and cognitive development suggests that students need effective instruction in order to use any type of external representations correctly (Fueyo & Bushell, 1998;Sowell, 1989; Uttal, Scudder, & DeLoache, 1997). Brief instruction on the nature of the particular visual representation may not be sufficient (Rittle‐Johnson & Koedinger, 2001), but more effective representation‐specific instruction could be time consuming, and may not transfer to other novel representations that students encounter.…”

Persistent and Pernicious Errors in Algebraic Problem Solving

“…Similarly, there is some evidence to suggest that the use of Algebra Tiles can help students understand variables and like terms (Confrey & Lanier, 1980;Kitt & Leitze, 1992; but see Askey, 1999); Belenky and Nokes (2009) also found that the use of manipulatives helped students correctly identify variables in algebraic word problems. As with all manipulatives, one issue is that teachers must take time to instruct students about the representations or manipulatives before they are used (Fueyo & Bushell, 1998;Uttal, Scudder, & DeLoache, 1997); if students are not adequately familiar with the materials, helpful tools can quickly become a hindrance (Booth & Koedinger, 2012). Classroom time constraints must be considered when interventions are developed; even concept-based interventions which do not require familiarization with alternative representations take time.…”

Peer Tutoring to Prevent Firearm Play: Acquisition, Generalization, and Long‐term Maintenance of Safety Skills

“…Peer tutoring has been used to deliver instruction in a variety of areas, including academic, social, and behavioral skills (e.g., Anhalt, McNeil, & Bahl, 1998;Flood, Wilder, Flood, & Masuda, 2002;Fueyo & Bushell, 1998;Gumpel & Frank, 1999;Pigott, Fantuzzo, & Clement, 1986;Trovato & Bucher, 1980). The positive results demonstrated in the literature have clear implications for the use of peer tutoring to teach skills to children to prevent firearm injury.…”