The Development and Validation of a Diagnostic Assessment of Algebraic Thinking Skills for Students in the Elementary Grades

Thesis (Ph.D.)--University of Washington, 2013Elementary school students often exhibit a wide variety of different conceptions associated with algebraic thinking that their teachers fail to recognize or understand (Smith, diSessa, & Roschelle, 1994). It is crucial that elementary school teachers possess knowledge of the variety of different student conceptions and also boast abilities to address alternative conceptions, as students who are not provided with opportunities to think algebraically may continue to struggle with algebra throughout school (National Council of Teachers of Mathematics [NCTM], 2000; Smith et al., 1994). The purpose of this research, therefore, is to create and validate a diagnostic assessment tool for the elementary grades that can be used to help teachers better recognize and understand algebraic thinking conceptions. Although several researchers have created non-validated assessment items for use in intervention research (i.e., Jacobs et al., 2007) and others have begun work creating an algebraic thinking diagnostic tool for the middle and high school grades (i.e., Russell et al., 2009), no formally validated algebraic thinking diagnostic tools were discovered for elementary school students. Further, it appears that very few, if any, of the research studies conducted around algebraic thinking featured random samples or large sample sizes. Because of these gaps in the research, this inquiry seeks to address the following research purposes: 1) Validate a diagnostic assessment tool for measuring the algebraic thinking skills of elementary school students; 2) Investigate the algebraic thinking skills elementary students currently possess; and 3) Cross-culturally validate this diagnostic assessment tool with students in Singapore. A random stratified cluster sample was therefore used in this study, with 1,745 elementary school students in grades 1-5 from six different schools in six different school districts in urban Washington State completing a diagnostic assessment of algebraic thinking skills. Teachers of these students completed two teacher surveys regarding their views towards teaching algebraic thinking skills and their use of the assessment results. An additional convenience sample of 1,619 students in grades 1-6 from four different schools in Singapore completed the diagnostic assessment. An additional convenience sample of 73 students in grades 1-5 from two different schools in urban Washington State were interviewed via a `think-aloud protocol' to better understand student thinking while completing the assessment. Initial results demonstrated that the results of this assessment tool may be reliable and valid for the purposes described. Results indicated that although students experienced alternative conceptions discovered by other researchers, these were not occurring at nearly as high of rates as previously reported. Further results and the implications of these findings will be discussed