This study describes 3 years of mathematics intervention research examining the effectiveness of a summer individualized tutoring program for rising fourth-, fifth-, and sixth-grade students with low mathematics achievement. Based on an iceberg model of learning, an instructional framework was developed that identified and targeted students’ specific mathematical needs, developed number sense flexibility, and encouraged positive mindset or disposition. Students participated in eight one-on-one tutoring intervention sessions. Pre- and posttest results indicated that students made moderate to large effect size gains in each targeted area of instruction. Additionally, the intervention proved to produce positive results across three different contexts for delivering tutoring instruction.
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References
1.
BillsC. (2003). Errors and misconceptions in KS3 ‘number.’Proceedings of the British Society for Research into Learning Mathematics, Londres, 23(3), 7–12.
2.
BloteA. W., KleinA. S., & BeishuizenM. (2000). Mental computation and conceptual understanding.Learning and Instruction,10, 221–247.
3.
CarpenterT. P., FrankeM. I., JacobsV. R., FennemaE., & EmpsonS. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction.Journal for Research in Mathematics Education,29(1), 3–20.
4.
ClaytonG. A., BurtonK., WilsonB., & NeilM. (1988). Effective mathematics teaching: Remediation strategies: Grades K-5.Triangle Park, NC: Southeastern Educational Improvement Research Lab.
5.
CottonT. (2004). Inclusion through mathematics education.Mathematics Teaching,187(June), 35–40.
6.
CreswellJ. W., & ClarkV. L. P. (2007). Designing and conducting mixed methods research.Thousand Oaks, CA: Sage.
7.
DettoriG., & OttM. (2006). Looking beyond the performance of grave underachievers in mathematics.Intervention in School and Clinic,41(4), 201–208.
8.
DowkerA. (2001). Numeracy recovery: A pilot scheme for early intervention with young children with numeracy difficulties.Support for Learning,16(1), 6–10.
9.
DowkerA. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education.New York, NY: Psychology Press.
10.
Ellemor-CollinsD., & WrightR. (2007). Assessing pupil knowledge of the sequential structure of numbers.Educational and Child Psychology24(2), 54–63.
11.
FuchsL. S. (2005). Prevention research in mathematics: Improving outcomes, building identification models, and understanding disability.Journal of Learning Disorders38(4), 350–352.
12.
FusonK. C. (1990). Issues in place-value and multidigit addition and subtraction learning and teaching.Journal for Research in Mathematics Education, 21(4), 273–280.
13.
GadanidisG. (2004). The pleasure of attention and insight.Mathematics Teaching,186, March, 10–13.
14.
GearyD. C. (2010). Mathematical disabilities: Reflections on cognitive, neuropsychological, and genetic components.Learning and Individual Differences,20(2010), 130–133.
15.
GerstenR. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities.Journal of Special Education,44, 18–28.
16.
GerstenR., & Newman-GoncharR. (2011). Understanding RTI in mathematics: Proven methods and applications.Reston, VA: National Council of Teachers of Mathematics.
17.
KeF., & GrabowskiB. (2007). Gameplaying for maths learning: Cooperative or not?British Journal of Educational Technology, 38(2), 249–259.
18.
MaL. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States.Mahwah, NJ: Erlbaum.
19.
MarkovitsZ., & SowderJ. (1994). Developing number sense: An intervention study in grade 7.Journal for Research in Mathematics Education, 5(1), 4–29.
20.
NardiE., & StewardS. (2002). I would be the best mathematician in the world … if I actually enjoyed it.Mathematics Teaching,179, 41–44.
21.
National Research Council, Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. (2001). The strands of mathematical proficiency. In KilpatrickJ., SwaffordJ., & FindellB. (Eds.), Adding it up: Helping children learn mathematics (pp. 115–155). Washington, DC: National Academy Press.
22.
PattonM. Q. (1990). Qualitative evaluation and research methods (2nd ed.). Newbury Park, CA: Sage.
23.
ShumwayJ. F. (2011). Number sense routines: Building numerical literacy every day in grades K–3.Portland, ME: Stenhouse Publishers.
24.
StraussA. L., & CorbinJ. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques.Thousand Oaks, CA: Sage.
25.
ThrelfallJ. (2002). Flexible mental calculation.Educational Studies in Mathematics,50(1), 29–47.
26.
Van De WalleJ. A. (2004). Elementary and middle school mathematics: Teaching developmentally.Boston, MA: Pearson Education.
27.
VarelasM., & BeckerJ. (1997). Children's developing understanding of place value: Semiotic aspects.Cognition and Instruction,15(2), 265–286.
VaughnS. (2011). Foreword. In GerstenR., & Newman-GoncharR. (Eds.), Understanding RTI in mathematics: Proven methods and application (pp. xv–xvi). Reston, VA: National Council of Teachers of Mathematics.
30.
VosniadouS., & BrewerW. F. (1987). Theories of knowledge restructuring in development.Review of Educational Research,57(1), 51–67.
31.
VygotskyL. S. (1978). Mind in society: The development of higher psychological processes.Cambridge, MA: Harvard University Press.
32.
WebbD. C., BoswinkelN., & DekkerT. (2008). Beneath the tip of the iceberg: Using representations to support student understanding.Mathematics Teaching in the Middle School,14(2), 110–113.
33.
WestenskowA. (2012). Equivalent fraction learning trajectories for students with mathematical learning difficulties when using manipulatives (Doctoral Dissertation, Utah State University, Logan, Utah).
34.
WestenskowA., Boyer-ThurgoodJ., & Moyer-PackenhamP. S. (2015). A window into mathematical support: How parents’ perceptions change following observations of mathematics tutoring.Journal of Research in Childhood Education,29(4), 458–475.
35.
WestenskowA., & Moyer-PackenhamP. (2016). Using an iceberg intervention model to understand equivalent fraction learning when students with mathematical learning difficulties use different manipulatives.The International Journal for Technology in Mathematics Education, 23(2), 45–63.
36.
WestenskowA., Moyer-PackenhamP. S., & ChildB. (2014, January). Developing number sense flexibility: Effectiveness of a Tier II summer intervention program.Proceedings of the 12th Annual Hawaii International Conference on Education (pp. 1193–1201), Honolulu, Hawaii.
37.
YangD. C. (2003). Teaching and learning number sense—an intervention study of fifth grade students in Taiwan.International Journal of Science and Mathematics Education, 1(1), 115–134.
38.
Young-LoveridgeJ. M. (2004). Effects on early numeracy of a program using number books and games.Early Childhood Research Quarterly, 19(1), 82–98.
