## MODULE(S^{2}) Curriculum Materials: Supporting Program Transformations Involving Secondary Content Courses

*Supplementary Materials for AMTE Standards*

MODULE(S^{2}) curriculum materials are generated through a National Science Foundation funded project aimed at building connection between content courses for prospective secondary teachers and the high school mathematics content they will teach. The full curriculum materials support AMTE’s Standards for Preparing Teachers of Mathematics (SPTM; AMTE, 2017) by exemplifying work that centers on innovation in programmatic structures and practices and address a variety of the SPTM program standards and indicators. The MODULE(S^{2}) project is a collaboration among mathematicians, statisticians, mathematics educators, statistics educators, and K-12 teachers around curriculum for content courses required of secondary mathematics teachers in preparation programs. The materials shared here include excerpts of curricular materials for Algebra, Geometry, Modeling, and Statistics designed by collaborative groups of stakeholders. Also included are suggested supports for collaboration and programmatic transformation regarding advanced mathematics content courses offered in secondary preparation programs.

The MODULE(S^{2}) project is focused on the development of prospective secondary mathematics teachers’ (PSMTs’) mathematical knowledge needed for teaching (MKT; Ball et al., 2008; Rowland, 2013) within upper-level content courses. The work of the project aims to address the identified problems that 1) PSMTs often do not find connection between upper-level mathematics content courses and teaching secondary mathematics (Goulding et al., 2003; Zazkis & Leikin, 2010) and 2) PSMTs must deeply understand the mathematics they are going to teach and learn it in a way that is consistent with expectations of them as teachers (Banilower et al., 2013).

In response to these problems, the project grew out of the Mathematics Teacher Education Partnership. Through collaboration with mathematicians, mathematics educators, and K-12 teachers we designed twelve educative curriculum (Davis & Krajcik, 2005) modules in the content areas of Geometry, Algebra, Statistics, and Mathematical Modeling. Each module includes opportunities for PSMTs to engage in mathematical tasks that are explicitly set in pedagogical settings for the purpose of developing PSMTs’ MKT. These simulation of practice opportunities involve both video and written responses and provide opportunities to observe and then develop PSMTs’ MKT. In addition, the materials include connection to K-12 learning standards, examples of activities appropriate for K-12 learning, and opportunities to examine K-12 learner thinking in the context of the content for the course. These features are interwoven with rigorous exploration of mathematical concepts. The instructor materials provide suggestions for implementing the materials using equitable teaching practices and, where appropriate, content is explored through a lens of social justice applications. Each of the modules is designed as a stand-alone unit, so that programs may choose to select modules from different content areas to serve instructional needs unique to the program.

In the excerpts included here, we provide the following for each of the four content areas (Algebra, Geometry, Modeling, and Statistics):

1. An overview of the entire course, including a description of each of the three modules for the specific content area,

2. An overview of the module from which the lesson excerpt is drawn, including the learning goals of the module, and a brief description of the lessons within the module,

3. A lesson excerpt, including description of the overall lesson and student handouts.

**Documents for Mathematics Teacher Educators**

**Overview of MODULE(S ^{2}) Materials**

**Statistics curriculum materials**

**Standards and Indicators these Materials Target**

Use of these materials across all four content areas and in multiple programs within preparation programs supports the SPTM in both content and partnership standards.

- C.1. Mathematics Concepts, Practices and Curriculum. These materials support mathematics departments to engage PSMTs in coursework in which they learn rigorous and relevant mathematical content which both connects to secondary content they will teach and goes deep into mathematical reasoning and foundations of that content.
- C.1.4 Analyze the Mathematical Content of Curriculum. Opportunities to examine standards and curriculum documents are embedded within the materials along with simulation of practice activities which engage PSMTs in examining K-12 students’ thinking around the mathematical ideas explored.
- C.1.5 Analyze Mathematical Thinking. The materials include samples of student thinking that offer opportunity to observe and analyze different approaches to mathematical problems. Responding to these samples requires PSMTs to build from student thinking and consider a range of potential learner responses.

- C.2. Pedagogical Knowledge and Practices for Teaching Mathematics.
- C.2.1 Promote Equitable Teaching. The instructor materials include explication of equitable teaching practices to support the users of these materials (both mathematicians and mathematics educators) in implementing equitable teaching practices so that PSMTs experience learning in the ways they will be expected to teach

- C.3 Students as Learners of Mathematics:Throughout the MODULE(S
^{2}) materials, we incorporate opportunities to examine student thinking within the context of the mathematical concepts being developed. This provides opportunities to build understanding of learner thinking at the same time as PSMTs deepen their own understanding of the concepts.- C.3.1 Anticipate and Attend to Students’ Thinking About Mathematics Content. The materials include opportunities to consider frameworks that describe how students learn mathematical concepts (e.g., van Hiele model) and also provide activities in which PSMTs anticipate learners’ responses to mathematical tasks and then plan for moving learning forward through questioning and exploration.

- C.4 Social Contexts of Mathematics Teaching and Learning. Within the materials, we have incorporated problems in contexts that bring attention to injustice through mathematical investigations, particularly in Statistics and Modeling materials. In addition, we offer opportunities to analyze diverse ways of thinking that can be opened into conversations that cultivate positive mathematical identities. Activities are structured with pedagogical practices that support building positive mathematical identities.
- P.1 Partnerships. This project grew out of the Mathematics Teacher Education Partnership, which leverages the knowledge and experience of stakeholders at a variety of levels: mathematicians, mathematics educators, K-12 teachers, and others.
- P.1.1 Engage all Partners Productively. Our author teams include multiple stakeholders (K-12 faculty, mathematics educators, and mathematicians). Through the materials, we demonstrate the types of products that can be accomplished with a partnership among multiple stakeholders.
- P.1.2 Provide Instructional Support. Alongside the materials, we provide instructor support for faculty teaching with the materials including professional development experiences and written instructor materials, which support institutions in making programmatic changes to include content courses with a focus on secondary teaching.

- P.2 Opportunities to Learn Mathematics. These materials are developed as rigorous, content courses that promote deep understanding of mathematical concepts while also making connection to mathematics taught in secondary schools.
- P.2.1 Attend to Mathematics Content Relevant to Teaching. When developing content in the materials we attended to content in the Common Core State Standards for Mathematics (National Governors Association and Council of Chief State School Officers, 2010) and research in the field to focus our materials on advanced mathematics content that has applications to teaching school mathematics.
- P.2.2 Build mathematical Practices and Processes. We structure the progression of activities in our materials to center instruction on PSMTs exploring conjectures and justification and the instructors using students’ explanations, justifications, and representations in their course teaching. Supports are provided in the instructional materials for faculty to use these techniques.
- P.2.3 Provide Sustained, Quality Experiences. We utilize simulations of teaching practice throughout each content area and across all content areas to provide sustained opportunities for PSMTs’ to apply their advanced mathematical understandings to the work of teaching school mathematics and the instructional materials provide support for instructors to enact these activities.

- P.3. Opportunities to Learn to Teach Mathematics. By incorporating simulation of teaching practice activities across the materials (at least two activities in each of the 12 modules) the materials provide a vision for how opportunities to learn to teach mathematics can be utilized by both mathematicians and mathematics educators in content courses for PSMTs. In addition to these simulations of practice, there are instances of unpacking the ways in which learners typically think and learn about particular concepts

## About the Authors

**Emina Alibegovic - Rowland Hall School****Cynthia Anhalt - University of Arizona****Jason Aubrey - University of Arizona****Stephanie Casey - Eastern Michigan University****Ricardo Cortez - Tulane University****James Hart - Middle Tennessee State University****Brynja Kohler - Utah State University****Yvonne Lai University of Nebraska-Lincoln****Alyson Lischka - Middle Tennessee State University****Cody Patternson - Texas State University****Andrew Ross - Eastern Michigan University****Jeremy Strayer - Middle Tennessee State University**