Indicators of Multiplicative Reasoning among Fourth Grade Students

Carrier, J. (2010)Under the direction of Dr. Sarah B. Berenson and Dr. Kerri Richardson. University of North Carolina, Greensborough, NC

PROBLEMSDevelopment of multiplicative thinking is

a key construct for understanding advance mathematic topics (Confrey, 1994; Lamon, 1994; Harel & Sowder, 2005) .

Many US elementary school teachers have limited understanding about the mathematics they teach (Ball, 1990; Post, Harel, Behr & Lesh, 1993; Tall 1991).

Students encounter difficulties as they move into more advance mathematical thinking.

COGNITIVE ROOTS OF MULTIPLICATIVE REASONINGrepeated addition( Steffe, 1994)splitting (Confrey &Smith, 1994) relational understanding(Clark &

Kamii, 1991).

THEORETICAL FRAMEWORK

an adapted framework (Thorton &Fuller, 1981; Karplus &Lawson, 1974; Clark & Kamii, 1996) that specified multiplicative reasoning levels.

Level 1: Spontaneous StrategyLevel 2: Additive Strategy Level 3: Multiplicative Strategy without

Success Level 4: Multiplicative Strategy with

Success Level 5: Proportional Strategy

RESEARCH QUESTIONSWhat are the indicators of

multiplicative reasoning among fourth grade students?

What strategies do fourth grade students utilize in solving multiplicative reasoning word problems?

What multiplicative reasoning strategies do the items on the test instrument invoke in fourth grade students?

METHODOLOGYPiaget stated that students cannot

present multiplicative reasoning until they reached the 4th stage of the development; formal operations stage ages 11-12 (predominantly in 5th grade).

Author conducted a pilot study in 2008 with four promising 4th grader students (ages 9 and 10) to test the five levels of multiplicative reasoning.

METHODOLOGY CONT..a qualitative study : Conducted

interviews with 15 4th grade students (ages 9-10) from a charter I school in a large urban school district in NC

10 questions were developed using Microsoft Visio

Computer was used as a medium for interviews.

Cross case analysis of 10 itemsResponse analysis of each student

FINDINGSresearch elaborated, diagnosed

and classified indicators of multiplicative reasoning of 4th grade students and categorized these indicators from least to most sophisticated ones

CRITIQUE clearly formulated research problems laid a body of evidences from the existing

literature to address the problemDid not discuss in detail why

multiplicative reasoning so important for advance mathematics understanding

provided context for the research questions

identified and critically analyzed the related works addressed the gaps

CRITIQUE CONT… author’s strict interpretation of formal

operation development stage limits the extension of the study

Did not clearly statedthe audience of this researchhow other people use the findings of the

study how this study help teachers, policy

makers and researcher to make smart decisions on curriculum development and instruction

REFLECTIONa search of literature is critical to identify

what has been done, what are the gaps in existing literature needs to be filled and to define your research problems and questions.

broader perspective to set up specific points of interest of the study

theoretical background of the study is critical part of the literature review that serve a foundation for subsequent actions in the study; your methodology selection, your way of reporting findings

REFLECTION CONT…careful about the scope of the

researcha smart flow within the literature

review toward accomplishing purpose of the study.

QUESTIONS?