Date of Award

Fall 12-14-2023

Document Type

Project (696 or 796 registration)

Degree Name

Master of Science in Curriculum & Instruction


Graduate Studies

Committee Chair

Kathy Enger


This quantitative study used a pretest and posttest quasi-experimental design to investigate how students’ understanding of algebraic concepts compared when they were taught using invention and consolidation phases or traditional direct instruction. It also explored how students’ beliefs and attitudes toward mathematics were affected by learning through invention and consolidation phases through a survey with a Likert scale. The study took place during the 2022-2023 academic year in the Intermediate Algebra II course at a mid-size public high school in Minnesota. The researcher had two sections of the course and taught one through direct instruction and the other through invention and consolidation phases. The study consisted of four rounds on four different algebra topics. The direct instruction group learned the concepts and procedures first and then solved problems. The invention and consolidation group worked to solve problems first by exploring ideas and applying problem-solving strategies and then consolidated their learning through direct instruction. Mann-Whitney U tests and independent sample t-tests were used to compare the mean scores on the pretest and posttest, the amount of growth made from the pretest to posttest, and students’ attitudes and beliefs about mathematics. The results show that students learning through invention and consolidation phases either scored higher on the posttest or made more growth than students learning through direct instruction on three out of the four topics with some statistically significant differences on questions assessing conceptual understanding. Students also slightly improved their beliefs and attitudes around mathematics, but the differences were not statistically significant.



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