Number Sequences as Explanatory Models for Middle-Grades Students' Algebraic Reasoning

Early algebraic reasoning can be viewed as developing a bridge between arithmetic and algebra. Accordingly, this research examines how middle-grades students' arithmetic reasoning, classified by their number sequences, can be used to model their algebraic reasoning as it pertains to generalizing, writing, and solving linear equations and systems of equations. In the quantitative phase of research, 326 students in grades six through nine completed a survey to assess their number sequence construction. In the qualitative phase, 18 students participated in clinical interviews, the purpose of which was to elicit their algebraic reasoning. Results show that the numbers of students who had constructed the two least sophisticated number sequences did not change significantly across grades six through nine. In contrast, the numbers of students who had constructed the three most sophisticated number sequences did change significantly from grades six and seven to grades eight and nine. Furthermore, students did not consistently reason algebraically unless they had constructed at least the fourth number sequence. Thus, it is concluded that students with the two least sophisticated number sequences are no more prepared to reason algebraically in ninth grade than they were in sixth.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Curriculum and Instruction

Department dc:contributor.department

Education, Vocational-Technical

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2019

Author dc:creator

• Zwanch, Karen Virginia

Chair dc:contributor.committeechair

• Wilkins, Jesse L. M.

Committee members dc:contributor.committeemember

• Ulrich, Catherine L.
• Billingsley, Bonnie S.
• Norton, Anderson H. III

• Number
• Algebraic Reasoning

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:19321

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/96421