BS+Course+Learning+Outcomes

=Course Learning Outcomes= Each course should have 3-5 LOs. Each LO should be tied to one or more program LOs. The person whose name is bolded is responsible for the initial draft of the LOs and for coordinating feedback with other people who have taught the course.

MTHED 177 Critical Review of School Mathematics
Description: Strengthen understanding of high-school mathematics; gain awareness as mathematics learners in learning communities; learn how to support collaborative communities as teachers. (**Dan**, Hope, Scott, Blake, Keith) Students have a deep understanding of select central concepts in middle school mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching these select concepts. || 1 || Students can engage in meaningful mathematical exploration, are willing and able to approach and solve challenging mathematics problems, and can reflect on their own learning to make inferences about how adolescents learn mathematics. || 1, 2 || Students know and can describe what it means to understand mathematics relationally, can demonstrate mathematical understanding by creating and evaluating conceptually-oriented mathematical explanations, and can explain why conceptually-oriented mathematics instruction is essential for supporting adolescents' learning of mathematics. || 1, 2 || Students recognize that mathematics instruction that does not build relational understanding has failed a majority of adolescents, even themselves, and that they have a moral obligation to seek the necessary knowledge and expertise to teach mathematics in ways that enable all adolescents to develop conceptual understanding, procedural fluency, and facility with authentic mathematical practices. || 2, 5, 6 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Mathematical Exploration**
 * 3 || **Mathematical Understanding**
 * 4 || **Mathematics Instruction**

MTHED 276 Exploration of Teaching
Field-based initial teaching experience directed at helping prospective teachers experience demands and opportunities associated with teaching secondary students. (**Scott**, LOC) Students understand authentic mathematical practices and use them to engage in meaningful mathematical exploration and reflect on their own use of these practices to make inferences about how adolescents might engage in mathematical tasks. || 1, 2, 3 || Students articulate a philosophy of teaching and learning mathematics based on the professional standards for teaching mathematics, the moral dimensions of teaching, and the INTASC standards. || 2, 3, 5, 6 || Students can use curriculum guides such as the NCTM content standards or the Common Core State Standards to trace the K-12 development of a select central concept of mathematics as a means for planning instruction appropriate to a particular grade level and topic. || 2, 3 || Students can analyze and describe the mathematical experiences of adolescents in terms of the tasks, discourse and learning environments they observe in public school classrooms, and can reconcile the theoretical principles of their university experience with the reality of a secondary classroom. || 2, 3, 4 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematical Practices**
 * 2 || **Philosophy of Teaching and Learning Mathematics**
 * 3 || **Aligning Curriculum and Instructional Goals**
 * 4 || **Analyzing Classroom Instruction**

MTHED 277 Task Design and Assessment of Student Understanding
Description: Building tasks that elicit important mathematical ideas. Reflecting on and assessing the success of tasks through questioning and other methods of formative assessment. (**Dan,** Blake, Hope, Scott, Keith) Students have a deep understanding of select central concepts in high school mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching these concepts. || 1 || Students can analyze a section in a textbook or curricular unit, a specific mathematical topic, or a task to identify and describe the important mathematical concepts and procedures related to that section, topic, or task. || 1, 3 || Students can use their knowledge of mathematics and how adolescents learn mathematics to analyze a task in order to anticipate the type of mathematics learning it might foster or reveal. || 1, 2, 3 || Students understand how mathematical tasks can support adolescents' development of conceptual understanding and procedural fluency, and can use that understanding to design mathematical tasks that allow adolescents to use their prior knowledge and experiences to develop understanding of particular concepts and procedures. || 2, 3 || Students understand how formative and summative assessment can be used to support adolescents' development of conceptual understanding and procedural fluency, and can use that understanding to design assessment tasks that provide evidence of and insight into adolescents' understanding of particular concepts and procedures. || 2, 4 || Students recognize and can explain how the thoughtful use of mathematical tasks can enable them to reflect on and improve their instruction, and how such use can nurture and empower adolescents to draw upon their divine potential, intelligence, and capabilities to learn and do mathematics. || 5, 6 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Identifying Concepts and Procedures**
 * 3 || **Task Analysis**
 * 4 || **Task Design for Learning**
 * 5 || **Task Design for Assessment**
 * 6 || **Task Design for Professional Growth and Stewardship**

MTHED 300 History and Philosophy of Mathematics
Description: Historical development of important mathematical ideas and philosophies; implications for the mathematical curriculum. (**Steve**, Dan, Hope) Students understand and can describe the major approaches—cultural, philosophical, and psychological—to explaining the origin and nature of mathematics and its relation to understanding and modeling the physical world. || 1 || Students understand and can describe the major historical periods of development of mathematical thought, as well as the contributions of various cultures and individuals within those periods. || 1 || Students understand and can describe the historical development of concepts and practices central to school mathematics, including numeration, arithmetic, algebra, geometry, calculus, and probability. || 1 || Through understanding the complex relationship between mathematical practices and human experience, students appreciate the complexity of teaching and learning mathematics and the different approaches and experiences adolescents will bring to learning those practices. || 2, 6 ||
 * || Course LO || Program LO ||
 * 1 || **Origin and Nature of Mathematics**
 * 2 || **Historical Periods and Contributions**
 * 3 || **Historical Development of Concepts and Practices**
 * 4 || **Complexity of Human Mathematical Activity and Learning**

MTHED 305 Basic Concepts of Mathematics
Description: Concept-oriented exploration of number, measurement, and informal geometry in relation to children's learning. (**Amy**, Doug, Blake) Students have a deep understanding of central concepts in elementary school mathematics related to whole numbers and whole number operations, number theory, integers and integer operations, geometry, and measurement; as well as core representations, canonical examples, patterns in children's thinking, and alternative algorithms germane to teaching these concepts. || 1, 2 || Students understand mathematics as a sense-making activity, can solve problems by employing conceptual understanding and mathematical reasoning, and can reflect on their own learning to make inferences about how children experience and understand mathematics. || 1, 2 || Students engage productively in mathematical inquiry, effectively communicate their mathematical ideas and reasoning with their peers, and reflect on the teaching practices modeled in the MthEd 305 classroom to make inferences about teaching practices that help children learn mathematics. || 1, 3 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Mathematical Thinking**
 * 3 || **Mathematical Activity**

MTHED 306 Concepts of Mathematics
Description: Concept-oriented exploration of rational numbers and proportional reasoning, probability, and early algebraic reasoning in relation to children's learning. (**Amy**, Doug, Blake) Students have a deep understanding of central concepts in elementary school mathematics related to fractions and fraction operations, probability, and early algebraic reasoning; as well as core representations, canonical examples, patterns in children's thinking, and alternative algorithms germane to teaching these concepts. || 1, 2 || Students understand mathematics as a sense-making activity, can solve problems by employing conceptual understanding and mathematical reasoning, and can reflect on their own learning to make inferences about how children experience and understand mathematics. || 1, 2 || Students engage productively in mathematical inquiry, effectively communicate their mathematical ideas and reasoning with their peers, and reflect on the teaching practices modeled in the MthEd 306 classroom to make inferences about teaching practices that help children learn mathematics. || 1, 3 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Mathematical Thinking**
 * 3 || **Mathematical Activity**

MTHED 308 Mathematics Teaching with Technology
Description: Using technology to teach and understand mathematics. Math-specific software and calculators used to investigate Euclidean geometry, non-Euclidean geometry, algorithms, probabilities, etc., research regarding effectiveness. (**Keith**, Blake, Doug, Hope, Scott) Students have a deep understanding of select central concepts in secondary mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching these select concepts. || LO 1 || Students can use technology to engage in meaningful mathematical exploration and can reflect on their own learning to make inferences about how adolescents learn mathematics with technology. || LO 1, 2 || Students can articulate and represent their mathematical thinking in technological environments in ways that are appropriate for their intended audience. || LO 1, 3 || Students understand the affordances and constraints of technology in teaching mathematics and can apply this knowledge to design learning opportunities involving the use of technology to support adolescents' mathematical learning. || LO 3 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Mathematical Exploration with Technology**
 * 3 || **Mathematical Communication**
 * 4 || **Instructional Design and Technology**

MTHED 362 Survey of Geometry
Description: Logical and historical development of Euclidean and non-Euclidean geometry, transformations and symmetry; relationships among axiomatic systems; use of software and other geometric models; proofs and Van Hiele levels. (**Steve**, Hope, Blake) Students understand central objects, concepts, relationships, definitions, and theorems of Euclidean geometry, how adolescents come to understand these, and the canonical examples and alternative approaches germane to teaching secondary school geometry. || 1, 2 || Students can communicate geometric ideas effectively using a variety of appropriate representations and can construct valid proofs of geometric theorems within a given axiom system. || 1 || Students understand and can describe the relationships among neutral, Euclidean, and non-Euclidean geometries in terms of fundamental geometric concepts, objects, and properties (particularly parallelism), and can use the fundamental properties of axiom systems and models to provide convincing arguments about these relationships. || 1 ||
 * || Course LO || Program LO ||
 * 1 || **Knowing and Learning Geometry**
 * 2 || **Communicating Geometric Ideas and Arguments**
 * 3 || **Multiple Geometries**

MTHED 377 Mathematics Teaching in the Public Schools
Description: Mathematics teaching practice in grades 7-12, including lesson/task design, curriculum evaluation, and classroom management in context of practice teaching. (**Keith**, Blake, Scott) Students understand the central concepts, tools of inquiry, and structures of the discipline of mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching secondary school mathematics. || 1 || Students can analyze a task, a section in a textbook or curricular unit, or a specific mathematical topic to identify and describe the related important mathematical concepts and procedures, and can design relevant tasks that foster conceptual understanding, procedural fluency, and authentic mathematical practices. || 1, 2, 3 || Students understand how to create lesson plans that involve meaningful tasks in the context of a given unit, that anticipate student thinking and how the lesson might build on that thinking, and that articulate how they will orchestrate each phase of the lesson (launch, explore, discuss, unpack). || 2, 3 || Students can use their lesson plans to engage adolescents in the day's activities (launch), facilitate meaningful exploration of mathematics (explore), orchestrate discussion that builds on and extends adolescents' emerging mathematical conceptions (discuss) and ensure the important mathematical concepts and procedures related to the goals of the lesson are made explicit (unpack). || 2, 3, 4 || Students understand how to design and use formative assessment that monitors the learner's progress, informs instructional decisions, and engages adolescents in assessing their own mathematical learning. || 4 || Students demonstrate their professionalism through maintaining appropriate relationships and behavior in the MthEd 377 classroom setting; improving practice through reflection and by providing, soliciting and incorporating feedback; and contributing to the professional learning community of the classroom. || 5 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Task Analysis and Design**
 * 3 || **Developing Lesson Plans**
 * 4 || **Orchestrating Lessons**
 * 5 || **Assessing Mathematical Learning**
 * 6 || **Professionalism**

MTHED 378 Practicum in Mathematics Education
Description: Implementing meaningful and engaging instruction for secondary students; developing critical thinking, problem solving, literacy, and democratic character; assessing learner performance. (**Keith,** Blake, Scott) Students understand that adolescents develop mathematical knowledge by building on prior knowledge and experience; that adolescents differ cognitively, linguistically, socially, emotionally, and physically; and that adolescents learn best when given regular opportunities to reason about and make sense of mathematics in an environment of high expectations and strong support. || 2 || Students understand how to design learning environments and mathematical experiences that engage all adolescents in the exploration and development of mathematical ideas, as well as how to effectively foster these environments and orchestrate these experiences by promoting conceptual understanding, procedural fluency, and authentic mathematical practices. || 3 || Students can analyze and describe the mathematical experiences of adolescents in terms of the tasks, discourse and learning environments they observe in public school classrooms, and can reconcile the theoretical principles of their university experience with the reality of a secondary classroom. || 2, 3, 4 || Students demonstrate their professionalism through maintaining appropriate relationships and behavior in the school setting, and improve their practice through reflection and by providing, soliciting and incorporating feedback. || 5 ||
 * || Course LO || Program LO ||
 * 1 || **Understanding of Mathematics Learners**
 * 2 || **Instructional Design for Mathematics Learning**
 * 3 || **Analyzing Classroom Instruction**
 * 4 || **Professionalism**

SC ED 476R Secondary Student Teaching
Capstone, field-based, semester-long experience in teaching secondary students; demonstrating proficiency in all program standards. Seminar required. (**Scott**, Bob) Students understand the central concepts, tools of inquiry, and structures of the discipline of mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching secondary school mathematics. || 1 || Students understand that adolescents develop mathematical knowledge by building on prior knowledge and experience; that adolescents differ cognitively, linguistically, socially, emotionally, and physically; and that adolescents learn best when given regular opportunities to reason about and make sense of mathematics in an environment of high expectations and strong support. || 2 || Students understand how to design learning environments and mathematical experiences that engage all adolescents in the exploration and development of mathematical ideas, as well as how to effectively foster these environments and orchestrate these experiences by promoting conceptual understanding, procedural fluency, and authentic mathematical practices. || 3 || Students understand how to design and use formative and summative assessments that monitor the learner's progress, inform instructional decisions, and engage adolescents in assessing their own mathematical learning. || 4 || Students demonstrate their professionalism through maintaining appropriate relationships and behavior in the school setting, and by seeking opportunities to improve practice and advance the profession through reflecting on practice, soliciting and incorporating feedback, and contributing to professional, school, and community organizations. || 5 || Students seek integrity between their personal and professional lives consistent with the restored gospel of Jesus Christ by recognizing all learners as children of God and striving to nurture their divine potential; applying gospel-centered principles of teaching and learning to family relationships, gospel service, and involvement in the community; and serving as examples of a Christ-centered life within their spheres of influence. || 6 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Understanding of Mathematics Learners**
 * 3 || **Instructional Design for Mathematics Learning**
 * 4 || **Assessment of Mathematics Learning**
 * 5 || **Professionalism**
 * 6 || **Spiritual Stewardship**

MTHED 495R Readings in Mathematics Education
Directed readings beyond scope of usual undergraduate courses. (**Dan**, LOC) Students have a deeper understanding of important issues and/or research in the field of mathematics education, and can use this new understanding to reevaluate their past and present experiences in mathematics classrooms, make connections to other important issues and problems in mathematics education, function more effectively in their role as an undergraduate research assistant, and/or reimagine their future experiences as a mathematics teacher. || 1, 2, 3 || Students recognize that there is an extensive body of literature on the learning and teaching of mathematics; can identify important authors, papers, issues, findings, theories, and limitations in a subfield of the literature; and recognize and value the need to remain current with developments in the field of mathematics education. || 5 ||
 * || Course LO || Program LO ||
 * 1 || **Applying Knowledge of Mathematics Education**
 * 2 || **Developing Professionalism**

SC ED 496R Academic Internship: Secondary Education
Capstone, field-based, year-long experience in teaching secondary students; demonstrating proficiency in all program standards. Seminar required. (**Scott**, Bob) Students understand the central concepts, tools of inquiry, and structures of the discipline of mathematics as well as core representations, canonical examples, and alternative algorithms germane to teaching secondary school mathematics. || 1 || Students understand that adolescents develop mathematical knowledge by building on prior knowledge and experience; that adolescents differ cognitively, linguistically, socially, emotionally, and physically; and that adolescents learn best when given regular opportunities to reason about and make sense of mathematics in an environment of high expectations and strong support. || 2 || Students understand how to design learning environments and mathematical experiences that engage all adolescents in the exploration and development of mathematical ideas, as well as how to effectively foster these environments and orchestrate these experiences by promoting conceptual understanding, procedural fluency, and authentic mathematical practices. || 3 || Students understand how to design and use formative and summative assessments that monitor the learner's progress, inform instructional decisions, and engage adolescents in assessing their own mathematical learning. || 4 || Students demonstrate their professionalism through maintaining appropriate relationships and behavior in the school setting, and by seeking opportunities to improve practice and advance the profession through reflecting on practice, soliciting and incorporating feedback, and contributing to professional, school, and community organizations. || 5 || Students seek integrity between their personal and professional lives consistent with the restored gospel of Jesus Christ by recognizing all learners as children of God and striving to nurture their divine potential; applying gospel-centered principles of teaching and learning to family relationships, gospel service, and involvement in the community; and serving as examples of a Christ-centered life within their spheres of influence. || 6 ||
 * || Course LO || Program LO ||
 * 1 || **Mathematics**
 * 2 || **Understanding Mathematics Learners**
 * 3 || **Instructional Design for Mathematics Learning**
 * 4 || **Assessment of Mathematics Learning**
 * 5 || **Professionalism**
 * 6 || **Spiritual Stewardship**

MTHED 497R Research in Mathematics Education
Undergraduate research experience. Faculty-supervised research. Written and oral presentation of findings required. (**Dan**, LOC) Students have a deeper understanding of the nature, design, and methods of research in the field of mathematics education; can make valuable contributions under limited supervision to the data collection and/or data analysis stages of faculty-directed mathematics education research; and can communicate their understanding of research in general, as well as of this specific research, through a scholarly oral or written report. || Grad LO || Students have a deeper understanding of a key issue or problem in the field of mathematics education, and can use this new understanding to reevaluate their past and present experiences in mathematics classrooms, make connections to other important issues and problems in mathematics education, function more effectively in their role as an undergraduate research assistant, and/or reimagine their future experiences as a mathematics teacher. || 1, 2, 3 || Students can identify their personal strengths and weaknesses in regards to conducting research in mathematics education, and have a sense for whether or not they would like to pursue more research opportunities through graduate study. || 5 ||
 * || Course LO || Program LO ||
 * 1 || **Engaging in Research**
 * 2 || **Applying Understanding from Research**
 * 3 || **Relating to Research**