College Algebra, Trigonometry, and Precalculus (Clayton)

This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1022/thumbnail.jp

High School 4th Mathematics: Precalculus for AP Calculus

ABSTRACT The purpose of this thesis is to provide the needed instructional materials to those who are teaching a Precalculus course following Algebra I, Geometry, and Algebra II. The recent adoption of the Common Core State Standards in Mathematics (CCSSM) has left many teachers scrambling to find instructional materials that meet the graduation requirement as well as insuring that our students are college and career ready when they leave high school. Furthermore, the College Board’s Advanced Placement (AP) Calculus curriculum is generally accepted as the model for a twenty-first century calculus course serving as prerequisite for STEM related fields of study at the college level. The path now needs to be set for a new precalculus course to align the AP goals and objectives with the CCSSM. For the 2014-2015 school year, high schools must offer AP courses in all four core content areas, math, ELA, science, and social studies (www.louisianabelieves.com). However, for students to be adequately prepared for AP Calculus there must be an effective precalculus course available to be taken first. This thesis, “High School 4th Mathematics: Precalculus for AP Calculus,” is written specifically with the goal of meeting this requirement. In Appendix C of this thesis, high school mathematics teachers are provided with comprehensive lecture notes that contain lesson plans and student activities that are aligned with AP Calculus ready, the CCSSM, and the Common Core State (+) Standards in Mathematics (CCS(+)SM). Each section of the lecture notes consists of a lesson plan that begins with a comprehensive overview of the major concepts, a list of the related CCSSM, a set of section learning objectives, lecture notes, and a variety of lesson activities that support the Common Core State Content Standards as well as Mathematical Practice Standards (MPS). Even though Appendix C can be used by any Precalculus teacher as a resource, it is designed specifically to go along with the textbook, Precalculus 8th Edition, written by Demana, Waits, Foley, and Kennedy, the textbook which will be used in 2014-2015 by Southeastern Louisiana University for its Dual Enrollment Precalculus course, Math 165

A Review of Secondary Mathematics Textbooks on Families of Functions

In 2008, twelve commonly used textbooks were studied for their use of technology and content across 5 families of functions: polynomial, rational, exponential, logarithmic, and trigonometric. Since 2008, the Common Core State Standards have been released and many textbook companies have used this as an opportunity to change their textbook content. This study reevaluates new high school algebra and precalculus textbooks across many of the same criterion studied in 2008. Some topics such as increasing and decreasing functions significantly increased their presence in the mathematics textbooks while topics such as sketching graphs has decreased. The reason for this shift in the content is unknown, but could be attributed to a change in emphasis of topics in the new Common Core State Standards

Making Mathematics Memorable, Meaningful, and Fun: Activities to Enhance Precalculus

To master material, students need to make it their own. As teachers, we should structure their interactions with mathematics in ways that are memorable, meaningful, and fun. One way to do this is to provide activities that stretch beyond the textbook and lead students to think and talk to one another about mathematics. This thesis contains a set of activities designed to enhance a precalculus course, along with solutions and feedback on each activity

Implications of an Iterative Design Experiment in Transcendental and Polynomial Functions Within a Flipped Classroom

This study explores an iterative design research experiment of a flipped mathematics classroom over the span of five curricular units involving big ideas of transcendental and polynomial functions. Transcendental and polynomial functions involve an algebraic, analytic, and graphical approach to the concepts and procedures of exponential, logarithmic, power, cubic, quadratic, linear, and rational functions. The Compleat design research methodology (Middleton, Gorard, Taylor, & Bannan-Ritland, 2008) was used to explore a series of instructional sequences that an instructor implemented in a flipped classroom while teaching big ideas of transcendental and polynomial functions. The experiment occurred over the course of a sixteen-week semester. Data analysis was constructed from a triangulation of relevant data from student constructions in the form of written documents, whole-group and small-group discussions from the video recordings, and the instructor’s personal reflective notes. The hypothetical learning trajectory served as the empirical basis upon which reflections occurred and meaningful modifications were made to the original prototype. Segmenting the content helped decrease the extraneous cognitive load by reducing the burden on students’ working memory in order to make instructional activities more meaningful and effective. More time was allocated in class for basic algorithmic processes prior to the implementation of the higher-order instructional tasks in phase five to account for the increasing intrinsic cognitive load in the instructional tasks. Micro-level practice-based concerns and improvements to the prototype as well as the creation of a theoretical and empirically-based instructional model were natural consequences to the design experiment

High Cognitive Demand Examples in Precalculus: Examining the Work and Knowledge Entailed in Enactment

Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a three-part study. To answer my research questions, I conducted classroom observations as well as pre- and post-observation interviews with seven graduate student instructors at a large public R1 university in the Midwest and used grounded theory to analyze my data. In the first component of the dissertation, I examine what high cognitive demand examples look like and identify three roles that instructors take on when enacting high cognitive demand examples: modeling, facilitating, and monitoring. In the second component, I decomposed the work of enacting high cognitive demand examples into five teaching tasks: attending to the mathematical point, making connections, providing clear verbal explanations, articulating cognitive processes, and supporting student understanding. Finally, in the third component, I examined the mathematical knowledge for teaching entailed in enacting examples and found that there are five domains of knowledge that support the maintenance of cognitive demand: knowledge of connections, representations, unpacking, students, and sequencing. These findings suggest ways in which we can help novice instructors enact high cognitive demand examples by focusing on the work and knowledge entailed in maintaining the cognitive demand. Advisor: Yvonne La

Characterizing Teacher Change Through the Perturbation of Pedagogical Goals

abstract: A teacher’s mathematical knowledge for teaching impacts the teacher’s pedagogical actions and goals (Marfai & Carlson, 2012; Moore, Teuscher, & Carlson, 2011), and a teacher’s instructional goals (Webb, 2011) influences the development of the teacher’s content knowledge for teaching. This study aimed to characterize the reciprocal relationship between a teacher’s mathematical knowledge for teaching and pedagogical goals. Two exploratory studies produced a framework to characterize a teacher’s mathematical goals for student learning. A case study was then conducted to investigate the effect of a professional developmental intervention designed to impact a teacher’s mathematical goals. The guiding research questions for this study were: (a) what is the effect of a professional development intervention, designed to perturb a teacher’s pedagogical goals for student learning to be more attentive to students’ thinking and learning, on a teacher’s views of teaching, stated goals for student learning, and overarching goals for students’ success in mathematics, and (b) what role does a teacher's mathematical teaching orientation and mathematical knowledge for teaching have on a teacher’s stated and overarching goals for student learning? Analysis of the data from this investigation revealed that a conceptual curriculum supported the advancement of a teacher’s thinking regarding the key ideas of mathematics of lessons, but without time to reflect and plan, the teacher made limited connections between the key mathematical ideas within and across lessons. The teacher’s overarching goals for supporting student learning and views of teaching mathematics also had a significant influence on her curricular choices and pedagogical moves when teaching. The findings further revealed that a teacher’s limited meanings for proportionality contributed to the teacher struggling during teaching to support students’ learning of concepts that relied on understanding proportionality. After experiencing this struggle the teacher reverted back to using skill-based lessons she had used before. The findings suggest a need for further research on the impact of professional development of teachers, both in building meanings of key mathematical ideas of a teacher’s lessons, and in professional support and time for teachers to build stronger mathematical meanings, reflect on student thinking and learning, and reconsider one’s instructional goals.Dissertation/ThesisDoctoral Dissertation Mathematics Education 201

Finding the Maximum and Minimum Magnitude Responses (Gains) of Third-Order Filters without Calculus

The maximum and minimum gains (with respect to frequency) of third-order low-pass and high-pass filters are derived without using calculus. Our method uses the little known fact that extrema of cubic functions can easily be found by purely algebraic means. PSpice simulations are provided that verify the theoretical results

Finding the Maximum and Minimum Magnitude Responses (Gains) of Third-Order Filters without Calculus

The maximum and minimum gains (with respect to frequency) of third-order low-pass and high-pass filters are derived without using calculus. Our method uses the little known fact that extrema of cubic functions can easily be found by purely algebraic means. PSpice simulations are provided that verify the theoretical results

Math Active Learning Lab: Math 107 Precalculus Notebook

This course notebook has been designed for students of Math 107 (Precalculus) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time. Topics in the Notebook are organized by weekly learning module. Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts. Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts. Completed Notebook is an invaluable tool when studying for exams.https://commons.und.edu/oers/1023/thumbnail.jp