Matching Items (2)
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- All Subjects: Student Thinking
- All Subjects: Mathematical Meanings
- All Subjects: Quantitative Reasoning
- Genre: Doctoral Dissertation
- Creators: Joshua, Surani Ashanthi
- Creators: Ramos, Richard K
- Member of: Theses and Dissertations
Description
This action research addressed teacher effectiveness in supporting students’ critical thinking skills by implementing differentiated instructional strategies in eight 3rd- and 4th-grade, self-contained, inclusive classrooms. This study addressed how third- and fourth-grade teachers perceived their instructional effectiveness, how differentiated instructional strategies influence third- and fourth-grade teachers, and how third- and fourth-grade teachers make further use of differentiated instruction to support students’ critical thinking skills across cultures, linguistics, and achievement levels to increase student achievement. Out of the enrollment in a southwest Phoenix elementary school, there was a 35% mobility rate; 76%, free and reduced lunches; 35%, Spanish-speaking homes; 10%, ELL services; and 10%, special education. The school was comprised of 52 certified teachers, out of which there were five related arts teachers, and four teachers who served gifted and special education students. Participants included all eight third- and fourth-grade teachers, 75% female and 25% males; 75% identified as Caucasian and 25% Hispanic/Latina, middle-class citizens. Professional development training was provided to these eight individual teachers during four months on differentiated instructional strategies to support students’ critical thinking. At this study’s beginning, these teachers perceived an obstacle to supporting students’ critical thinking as they struggled to learn new curriculums. Persevering through this challenge, teachers discovered success by implementing design-thinking, developing students’ growth mindsets, and utilizing cultural responsive teaching. These teachers identified three differentiated instructional strategies which impacted students’ academic progress: instructional scaffolds, collaborative group work, and project-based learning. Building upon linguistic responsive teaching, cultural responsive teaching, and Vygotsky’s socio-cultural theory, teachers revealed how to support students’ critical thinking through the use of graphic organizers, sentence frames, explicit instructions, growth mindsets, cultural references, and grouping structures. In addition, the outcomes demonstrated teachers can make further use of differentiated instruction by focusing on instructional groups, teachers’ mindsets, and methods for teaching accelerated learners. This study’s results have implications on teachers’ perception toward using differentiated instructional strategies as a viable method to support the multiple ways all students learn.
ContributorsRamos, Richard K (Author) / Liou, Daniel Dinn-You (Thesis advisor) / Dyer, Penelope (Committee member) / Saltmarsh, Sarah (Committee member) / McIntosh, Jason (Committee member) / Arizona State University (Publisher)
Created2018
Description
This dissertation reports three studies about what it means for teachers and students to reason with frames of reference: to conceptualize a reference frame, to coordinate multiple frames of reference, and to combine multiple frames of reference. Each paper expands on the previous one to illustrate and utilize the construct of frame of reference. The first paper is a theory paper that introduces the mental actions involved in reasoning with frames of reference. The concept of frames of reference, though commonly used in mathematics and physics, is not described cognitively in any literature. The paper offers a theoretical model of mental actions involved in conceptualizing a frame of reference. Additionally, it posits mental actions that are necessary for a student to reason with multiple frames of reference. It also extends the theory of quantitative reasoning with the construct of a ‘framed quantity’. The second paper investigates how two introductory calculus students who participated in teaching experiments reasoned about changes (variations). The data was analyzed to see to what extent each student conceptualized the variations within a conceptualized frame of reference as described in the first paper. The study found that the extent to which each student conceptualized, coordinated, and combined reference frames significantly affected his ability to reason productively about variations and to make sense of his own answers. The paper ends by analyzing 123 calculus students’ written responses to one of the tasks to build hypotheses about how calculus students reason about variations within frames of reference. The third paper reports how U.S. and Korean secondary mathematics teachers reason with frame of reference on open-response items. An assessment with five frame of reference tasks was given to 539 teachers in the US and Korea, and the responses were coded with rubrics intended to categorize responses by the extent to which they demonstrated conceptualized and coordinated frames of reference. The results show that the theory in the first study is useful in analyzing teachers’ reasoning with frames of reference, and that the items and rubrics function as useful tools in investigating teachers’ meanings for quantities within a frame of reference.
ContributorsJoshua, Surani Ashanthi (Author) / Thompson, Patrick W (Thesis advisor) / Carlson, Marilyn (Committee member) / Roh, Kyeong Hah (Committee member) / Middleton, James (Committee member) / Culbertson, Robert (Committee member) / Arizona State University (Publisher)
Created2019