Constructivism in Mathematics by Becky Buehner

What is Constructivism? Active learner – Constructs new knowledge through connecting their prior knowledge and instructed new knowledge Teacher assists – Prompting, leading questions, cueing, providing feeding, and modeling

What is Constructivism? Content – Authentic & Meaningful Assessment – Teacher preassesses – Ongoing – What does the learner need next Teacher needs knowledge of learner over content

Constructivist Video

Comparative Studies in Mathematics Illinois, K-6, rural setting Traditional vs. Constructivist Everyday Mathematics, Traditional Approach, Traditional Approach with support of Mountain Math (reinforces concepts K-2)

Comparative Studies in Mathematics No difference in outcomes between approaches African Americans outperformed strong implementation of the constructivist approach compared to African Americans who were given a weak implementation Narrowed achievement gap between African Americans and Caucasian students 1 st graders with Everyday Mathematics outperformed Chinese 1 st graders, but not Japanese 1 st graders

Comparative Studies in Mathematics Illinois, multiplication, third grade Constructivist vs. Traditional 4 classes – 2 classes received traditional methods 1 taught by regular educator and 1 taught by researcher – 2 classes received constructivist methods 1 taught by regular educator and 1 taught by researcher

Comparative Studies in Mathematics No statistical difference in approaches All showed growth Regular teacher expressed challenges – Using materials that students were unfamiliar with – Behavioral issues Researcher expresses having a classroom management plan before implementing a constructivist approach

Changing to a Constructivist Approach Europe, teachers filled out questionnaires about changing to a constructivist approach Education Council agreed that they needed to change to a constructivist theory – Change at the policy level Teachers need to be supportive in the change

Application Debbie Diller’s Math Work Stations Music and Movement Curriculums – Everyday Mathematics – Investigations in Number, Data, and Space

Demo Lesson Racing Addition – Move around game board and solve an addition problem when you move to a new space Sums to 8, 10, & 12 – Sort addition problems Dominoes – Find matches (same number of dots) – Match numeral to dots Hearts – Match numeral to dots

References Briars, D. J., & Resnick, L. B. (2000). Standards, assessments and what else? The essential elements of standards-based school improvement. Los Angeles: Center for the Study of Evaluation, Center for Research on Evaluation, Standards, and Student Testing, California University. Carroll, W. (2001). A longitudinal study of children in the curriculum. Evanston, IL: Northwestern University. Chung, I. (2004). A comparative assessment of constructivist and traditionalist approaches to establishing mathematical connections in learning multiplication. Education, 125(2), 271. Diller, D. (2011). Math work stations: Independent learning you can count on, K-2. Portland: Stemhouse Publishers. Dow, W. (2006). The need to change pedagogies in science and technology subjects: a European perspective. International Journal Of Technology & Design Education, 16(3), Grady, M., Watkins, S., & Montalvo, G. (2012). The effect of constructivist mathematics on achievement in rural schools. Rural Educator, 33(3), Mercer, C. D., & Jordan, L. (1994). Implications of constructivism for teaching math to students with moderate to mild disabilities. Journal Of Special Education, 28(3), 290. Peterson, P.L., Carpenter, T., & Fennama, E. (1989). Teachers’ knowledge of students’ knowledge in mathematics problem solving: Correlational and case analyses. Journal of Educational Psychology, 81, Scott, P. B. (1983). Perceived use of mathematics materials. School Science and Mathematics, 87(1), 21,24. Skoning, S. (2010). Dancing the curriculum. Kappa Delta Pi Record, 46(4),