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- Creators: Van de Sande, Carla
- Creators: Atkinson, Robert
- Status: Published
Description
This study empirically evaluated the effectiveness of the instructional design, learning tools, and role of the teacher in three versions of a semester-long, high-school remedial Algebra I course to determine what impact self-regulated learning skills and learning pattern training have on students' self-regulation, math achievement, and motivation. The 1st version was a business-as-usual traditional classroom teaching mathematics with direct instruction. The 2rd version of the course provided students with self-paced, individualized Algebra instruction with a web-based, intelligent tutor. The 3rd version of the course coupled self-paced, individualized instruction on the web-based, intelligent Algebra tutor coupled with a series of e-learning modules on self-regulated learning knowledge and skills that were distributed throughout the semester. A quasi-experimental, mixed methods evaluation design was used by assigning pre-registered, high-school remedial Algebra I class periods made up of an approximately equal number of students to one of the three study conditions or course versions: (a) the control course design, (b) web-based, intelligent tutor only course design, and (c) web-based, intelligent tutor + SRL e-learning modules course design. While no statistically significant differences on SRL skills, math achievement or motivation were found between the three conditions, effect-size estimates provide suggestive evidence that using the SRL e-learning modules based on ARCS motivation model (Keller, 2010) and Let Me Learn learning pattern instruction (Dawkins, Kottkamp, & Johnston, 2010) may help students regulate their learning and improve their study skills while using a web-based, intelligent Algebra tutor as evidenced by positive impacts on math achievement, motivation, and self-regulated learning skills. The study also explored predictive analyses using multiple regression and found that predictive models based on independent variables aligned to student demographics, learning mastery skills, and ARCS motivational factors are helpful in defining how to further refine course design and design learning evaluations that measure achievement, motivation, and self-regulated learning in web-based learning environments, including intelligent tutoring systems.
ContributorsBarrus, Angela (Author) / Atkinson, Robert K (Thesis advisor) / Van de Sande, Carla (Committee member) / Savenye, Wilhelmina (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation describes an investigation of four students' ways of thinking about functions of two variables and rate of change of those two-variable functions. Most secondary, introductory algebra, pre-calculus, and first and second semester calculus courses do not require students to think about functions of more than one variable. Yet vector calculus, calculus on manifolds, linear algebra, and differential equations all rest upon the idea of functions of two (or more) variables. This dissertation contributes to understanding productive ways of thinking that can support students in thinking about functions of two or more variables as they describe complex systems with multiple variables interacting. This dissertation focuses on modeling the way of thinking of four students who participated in a specific instructional sequence designed to explore the limits of their ways of thinking and in turn, develop a robust model that could explain, describe, and predict students' actions relative to specific tasks. The data was collected using a teaching experiment methodology, and the tasks within the teaching experiment leveraged quantitative reasoning and covariation as foundations of students developing a coherent understanding of two-variable functions and their rates of change. The findings of this study indicated that I could characterize students' ways of thinking about two-variable functions by focusing on their use of novice and/or expert shape thinking, and the students' ways of thinking about rate of change by focusing on their quantitative reasoning. The findings suggested that quantitative and covariational reasoning were foundational to a student's ability to generalize their understanding of a single-variable function to two or more variables, and their conception of rate of change to rate of change at a point in space. These results created a need to better understand how experts in the field, such as mathematicians and mathematics educators, thinking about multivariable functions and their rates of change.
ContributorsWeber, Eric David (Author) / Thompson, Patrick (Thesis advisor) / Middleton, James (Committee member) / Carlson, Marilyn (Committee member) / Saldanha, Luis (Committee member) / Milner, Fabio (Committee member) / Van de Sande, Carla (Committee member) / Arizona State University (Publisher)
Created2012
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
Description
The problem under investigation was to determine if a specific outline-style learning guide, called a Learning Agenda (LA), can improve a college algebra learning environment and if learner control can reduce the cognitive effort associated with note-taking in this instance. The 192 participants were volunteers from 47 different college algebra and pre-calculus classes at a community college in the southwestern United States. The approximate demographics of this college as of the academic year 2016 – 2017 are as follows: 53% women, 47% men; 61% ages 24 and under, 39% 25 and over; 43% Hispanic/Latino, 40% White, 7% other. Participants listened to an approximately 9-minute video lecture on solving a logarithmic equation. There were four dependent variables: encoding as measured by a posttest – pretest difference, perceived cognitive effort, attitude, and notes-quality/quantity. The perceived cognitive effort was measured by a self-reported questionnaire. The attitude was measured by an attitude survey. The note-quality/quantity measure included three sub-measures: expected mathematical expressions, expected phrases, and a total word count. There were two independent factors: note-taking method and learner control. The note-taking method had three levels: the Learning Agenda (LA), unguided note-taking (Usual), and no notes taken. The learner control factor had two levels: pausing allowed and pausing not allowed. The LA resulted in significantly improved notes on all three sub-measures (adjusted R2 = .298). There was a significant main effect of learner control on perceived cognitive effort with higher perceived cognitive effort occurring when pausing was not allowed and notes were taken. There was a significant interaction effect of the two factors on the attitude survey measure. The trend toward an improved attitude in both of the note-taking levels of the note-taking factor when pause was allowed was reversed in the no notes level when pausing was allowed. While significant encoding did occur as measured by the posttest – pretest difference (Cohen’s d = 1.81), this measure did not reliably vary across the levels of either the note-taking method factor or the learner control factor in this study. Interpretations were in terms of cognitive load management, split-attention, instructional design, and note-taking as a sense-making opportunity.
ContributorsTarr, Julie Charlotte (Author) / Nelson, Brian (Thesis advisor) / Atkinson, Robert (Committee member) / Savenye, Wilhelmina (Committee member) / Arizona State University (Publisher)
Created2018