**Course Materials For Instructors: Secondary**

This website provides access to materials for several courses developed as part of NebraskaMATH: Nebraska Algebra and New Teacher Network and the Nebraska Math and Science Summer Institutes at the University of Nebraska - Lincoln. The materials include a description and a complete set of documents needed to offer the course.

We believe good teaching matters, and teachers can improve their teaching practices when they strengthen their mathematical knowledge for teaching (MKT). MKT includes knowledge of mathematics, connecting that knowledge to secondary topics, knowledge of pedgagogy, and knowledge of adolescent psychology and development.

Anyone wishing to offer quality courses to secondary mathematics teachers for college credit or professional development may use and duplicate any of the materials (referencing NebraskaMATH when appropriate). In return, we ask that you let us know you have used the materials and provide us with feedback so that we might continually improve this and all courses.

Note: TEAC 892 is a course number that can be used for different courses, so we have offered multiple versions of TEAC 892 across time.

#### Math 804T-Math 808T Described on the Middle Level Page

Click here to go to the middle level courses page which includes descriptions of Math 804T, Math 805T, Math 806T, Math 808T, TEAC 800 and TEAC 801.

#### Math 807: Mathematics for High School Teachers Capstone I

This is a deep investigation of the connections between college-level calculus and abstract algebra and high school mathematics. The emphasis is on developing skills to see the connections between advanced math and high school math and then use this skill to help high school students explore and deepen their understanding of high school math concepts. The course will be workshop style with short lectures followed by lengthy guided group problem sets and discussions.

#### Math 808: Mathematics for High School Teachers Capstone II

This course builds on MATH 807 Capstone I, which is a deep investigation of the connections between college-level calculus and abstract algebra and high school mathematics, and adds a deep investigation into geometry. The emphasis is on developing skills to see the connections between advanced math and high school math and then use this skill to help high school students explore and deepen their understanding of high school math concepts. The course will be workshop style with short lectures followed by lengthy guided group problem sets and discussions.

#### Math 809: Mathematical Modeling for High School Teachers

This course is designed around a series of projects in which students examine the mathematics underlying several socially-relevant questions which arise in a variety of academic disciplines (i.e. real-world problems, such as how to use mathematics to understand the spread of a disease). Students learn to extract the mathematics out of the problem in order to construct models to describe them. The models are then analyzed using skills developed in this or previous mathematics courses. Note: this course is a high school version of Math 807T: Using Math to Understand our World, and is not appropriate for those who have already taken Math 807T.

#### Math 810T: Algebra for Algebra Teachers

The main goal of the course is to help Algebra I teachers better understand the conceptual underpinnings of school algebra, and how to leverage that understanding into improved classroom practice. Emphasis is placed on developing the habits of mind of a mathematical thinker.

#### Math 811T: Functions for Precalculus Teachers

A study of functions in the pre-calculus, high school mathematics curriculum from an advanced viewpoint. Functions will be investigated by examining their utility in more advanced courses and applications, enabling teachers to better understand the important aspects and appropriate emphasis of a concept. Content will include polynomial, circular (trig), and exponential functions, and their connections to calculus.

#### Math 812T: Geometry for Geometry Teachers

The main goals of the course are to strengthen your mathematical background for teaching Geometry. We will focus on undamental concepts of Euclidean geometry, with explorations of non-Euclidean geometry for contrast. We will make extensive use of manipulatives and the dynamic geometry software GeoGebra.

#### Stat 812T: Statistics for High School Teachers

This course will cover the statistical concepts typically taught in a high school Statistics class. These include: linear regression, two-way tables, sampling distributions, statistical inference for means and proportions, chi-square tests, and inference for regression. Some experience with basic statistical concepts (mean, standard deviation, elementary probability) is necessary. The course will be inquiry-based, and will emphasize applications and statistical thinking. Software and calculators will be used for most analyses. Note: this course is a high school version of Stat 811TT: Statistics for Middle Level Teachers, and is not usually appropriate for those who have already taken Stat 811T.

#### TEAC 800: Inquiry Into Teaching and Learning

This course will introduce you to the assumptions about what counts as knowledge underlying particular approaches to scholarly inquiry and will help you identify the factors, forces and audiences that shape any and all forms of educational research. TEAC 800 will also acquaint you with the dimensions that define the educational research agenda; familiarize you with the terminology, analytical tools and habits of mind that are needed to assess the appropriateness and credibility of various forms of educational inquiry; provide you with strategies to efficiently and effectively become a consumer (reader) of educational research and strengthen your professional writing skills; provide you with strategies and resources for conducting disciplined inquiry in an educational setting; and provide opportunities to make connections among the research methodologies that we discuss and the "real world" of educational decision- and policy-making.

#### TEAC 801: Curriculum Inquiry

The focus of this course for K-12 teachers will be on helping participants build an understanding of mathematics curriculum development, including historical and contemporary issues (such as the new Nebraska standards and the Common Core Standards in mathematics) that influence curriculum planning and educational change. The course is intended to provide a solid theoretical introduction to curriculum and suggest how this knowledge might be used in the teaching and learning of mathematics in the K-12 curriculum. The primary goal is to help participants develop a broader and deeper understanding of curriculum and curriculum inquiry as it relates to their own teaching practice.

#### TEAC 880E: Teaching Mathematics with Technology

The focus of this workshop is on developing skills for using GeoGebra and Excel in the teaching and learning of middle and high school mathematics. (A majority of the course will focus on GeoGebra, with lesser attention devoted to Excel.) Special attention will be given to topics found in Algebra, Geometry, Pre-Calculus and Calculus courses. Functions, transformations, conics, data analysis and other mathematics topics will be addressed. Participants will use GeoGebra to develop interactive mathematics applets.

#### TEAC 892: Integrating Teaching and Learning

This course will focus on the learning and teaching of functions and other key ideas in the ideas in the high school curriculum from algebra to introductory calculus. The goal is to explicitly apply the advanced mathematics learned to the improvement of classroom instruction. The course employs a variety of technologies in a modified Lesson Study design that repeatedly cycles through (1) the learning of a concept, (2) the development of an exemplary classroom lesson about the concept, and (3) the improvement of the lesson through reflection. May be taken concurrently with MATH 811T or Math 807.

#### TEAC 892: Teaching High School Statistics

The course will focus on current research and practices of teaching, learning and assessing statistics from multiple perspectives. Participating teachers will be challenged to understand statistics at a deeper level and become more effective through improved lesson design, reflection, and collaboration. This course is designed to be taken concurrently with Stat 811T or Stat 812T.

#### TEAC 892: Teacher Learning about Reasoning & Sense Making in Secondary Mathematics

This course will focus on three main issues: exploring the nature of reasoning-and-proving in secondary mathematics; establishing criteria for judging the validity of mathematical arguments; and, developing strategies for modifying current textbook tasks to provide more reasoning opportunities for students. Course materials include math tasks, cases drawn from real secondary mathematics classrooms, related student work, and prompts for mathematical and pedagogical discussions and reflections. This is an excellent course to help secondary teachers make immediate improvements to their mathematics classrooms in order to better prepare students for the NeSA-M.

The course was originally developed by Dr. Maragaret (Peg) Smith, a full professor in mathematics education from the University of Pittsburg, as part of an NSF funded grant entitled Cases of Reasoning-and-Proving in Secondary Mathematics (CORP).

"This is the first class that I have taken that focuses on how to use reasoning and proof in the classroom. I liked that we discovered and debated the difference between proof and rationale by looking at numerous examples of ‘proofs.’ To me, this has always been a gray area, and it was helpful to hear arguments from colleagues across the state. This is one of the best classes I have taken because the concepts that we learned can and should be used in all classrooms. The strategies are not specific for any one class, and have further stretched me as a teacher. You have the opportunity to learn a lot about yourself and improve the way you teach." Carrie Kopf, Norfolk Public Schools

#### TEAC 892: Integrating Geometry Teaching and Learning

The course focuses on current research and practices of teaching, learning and assessing geometry from multiple perspectives. Participating teachers will be challenged to understand geometry at a deeper level and become more effective through improved lesson design, reflection, and collaboration. This course is designed to be taken concurrently with Math 812T: Geometry for GeometryTeachers.

#### TEAC 949A: Mathematical Ways of Knowing and the Art of Teaching

In this advanced course, students will gain an understanding of the ways in which the field of mathematics has developed, how a variety of perspectives have impacted the questions and methods of mathematical inquiry, the development of mathematics as a school subject, and the role disciplinary knowledge plays in the teaching and learning of mathematics in schools. The course is organized in three parts. The first focuses on the history and nature of knowledge within a discipline, and how this knowledge is developed, justified, and construed. The second part examines readings, including some classic pieces on the role and place of knowledge in school. The third component explores the relationships between ways of knowing within a discipline and how teaching, learning, and knowing as a school subject is defined.

Topics addressed in the course include:

- The nature of knowledge in a discipline.
- How knowledge develops.
- What makes something true or accepted.
- The role of the community.
- The language of the field and how is it used.

Suggested prerequisites: TEAC 800 and TEAC 801 or equivalent experience with educational research.