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DEVELOPING ALGEBRA-READY STUDENTS FOR MIDDLE SCHOOL: EXPLORING THE IMPACT OF EARLY ALGEBRA !PRINCIPAL INVESTIGATORS: Maria Blanton Eric Knuth
[email protected] [email protected] http://www.terc.edu/staff/1666.html http://www.education.wisc.edu/ci/mathed
This project aims to build tools for investigating the impacts of early algebra education on students’ algebra readiness for middle grades. The primary project goals are 1.To coordinate research, curricular, and mathematical perspectives to design an Early Algebra Learning Progression [EALP] that identifies a curricular progression of core algebraic concepts across grades 3-7 and articulates trajectories in children’s thinking about these in grades 3-5. 2.Using the EALP, to design grade-based assessments of students’ algebra understanding for upper elementary and middle grades (grades 3-7) and to validate these assessments through psychometric testing. 3.To conduct a preliminary study concerning the impact of an early algebra intervention based on the EALP.
RESEARCH OBJECTIVES!
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RESEARCH OUTCOMES & PRODUCTS!
Project Goal 1: *Curricular progression for EALP Organized around the “Big Ideas” of • Generalized arithmetic • Equality, expressions, equations and inequalities • Functional thinking • Variable • Proportional reasoning and the algebraic thinking practices of • Generalizing • Representing generalizations • Justifying generalizations • Reasoning with generalizations Example for Grade 3 expectations of students:
Project Staff!
Angela Murphy Gardiner, TERC Isil Isler, University of Wisconsin Madison Timothy Marum, TERC Ana Stephens, University of Wisconsin Madison
*Available at project website: http://algebra.wceruw.org
RESEARCH OUTCOMES & PRODUCTS!
Project Goal 2: *Development of validated assessments for Grades 3-5 (Grades 6-7 assessments are in development) Assessments • are designed to test students’ understanding of the “Big Ideas”
as they increase in complexity across grades • are longitudinal in nature, so that growth in student
understanding can be determined • use primarily open-ended items in order to better document
students’ thinking Project Goal 3: Using our EALP, we conducted a one year-intervention
(approximately 20 lessons*) at each of grades 3-5. Students received the same grade 3-level intervention across all grades. Ten control and six experimental classrooms participated (n ~ 300).
Some findings: • No significant differences between experimental and control
students at pre-test*, but experimental students significantly outperformed control students at post-test* at each of grades 3-5 (p < 0.001), with most significant differences at grade 3.
At grade 3 (the grade level targeted by the intervention): • Experimental students significantly outperformed control
students on ALL items on the assessment except for #10e and #11. For both of these, experimental students outperformed control students, but not significantly.
• Significant gains in experimental students’ ability to think relationally about the equal sign. Control students continued to think operationally.
• Significant gains in experimental students’ ability to represent unknown quantities with variable expressions. No controls were able to use variables in any.
• Experimental students were more likely to recognize the underlying structure of fundamental properties and use this as a basis for justifying generalizations on a domain of numbers.
• Not only did experimental students significantly outperform control students in their ability to identify and describe function rules in words or variables, they were more likely to choose variables to represent their rule.
• Experimental students increasingly used strategies that reflected more algebraic (structural) approaches, while control students did not.
