The Standards for Mathematical Practice (SMP) Module and the Mathematics Classroom Practices Lesson Planning module (MCP-LP) are designed for secondary mathematics methods courses that have a companion clinical experience in a secondary (middle/high) school. The Modules in their current form, have been developed collaboratively within the Clinical Experiences Research Action Cluster of the Mathematics Teacher Education Partnership. The SMP and MCP-LP Modules consist of three activities each and are intended to take place over some in-class sessions, some out-of-class work which includes engaging the mentor teacher. However, mathematics preparation programs and methods instructors have implemented the Module in various scenarios based on the organization program structure and needs of their individual programs and students (Yow, Waller, & Edwards, 2019; Zelkowski, Yow, Ellis, & Waller, 2020). The first two activities are intended to be completed within methods courses with methods instructors with the third and final activity intended to engage the prospective secondary mathematics teachers’ (PSMTs) mentor teachers (MTs).
Documents for Mathematics Teacher Educators
This activity engages PSMTs in a discussion of current high school mathematics students’ habits of mind followed by a deeper dive into desired high school mathematics students’ habits of mind as detailed by the SMPs of the Common Core State Standards – Mathematics which encompasses the five NCTM process standards (Koestler, Felton-Koestler, Bieda, & Otten, 2013).
This activity involves PSMTs completing an inquiry based geometry task, facilitated by the methods instructor who models the SMPs during the task facilitation. Once the PSMTs have the opportunity to complete the task as students, the group uses a rubric to structure a discussion focused on the SMPs employed throughout the task. PSMTs also view and analyze an exemplar video of an actual classroom-based implementation of the task.
- PCMI Rubric
- SMP Look Fors
- Activity 2 Exit Slip
- SMP Activity 3 - You, your mentor teacher and the SMPs!
This activity concludes the three-part module by PSMTs viewing the exemplar video alongside their MTs in their clinical field experience classroom. PSMTs and MTs then discuss a sequence of questions intended to focus on the SMPs exhibited in the lesson and how those SMPs are or may be incorporated in the clinical experience setting.
This activity begins with the assumption that PSMTs will be engaging in their first lesson planning activity in their preparation program. The activity has the objective for methods instructors to learn, uncover, and understand potential unproductive beliefs that PSMTs may have about mathematics teaching and learning (NCTM, 2014). The activity engages PSMTs in considering an 8th grade or first-year algebra course assessment with the goal to compose a single lesson that ultimately would provide students the learning opportunities to be successful on the assessment
- MCP-LP Activity 1 - Supplemental Document for Pre-Lesson Planning
- MCP-LP Activity 1 - Lesson Plan Module Teacher Candidates
- MCP-LP Activity 1 - (TCs) Lesson Planning Module Assessment
- MCP-LP Activity 2 Professor/Instructor Instructions
This activity builds from the product produced by PSMTs in activity 1. PSMTs peer-collaborate in reviewing their drafted lesson plans utilizing a rubric derived from the MCOP2. The rubric allows both PSMTs and methods instructors to evaluate the drafted lesson plans ambitiousness of planning for the SMPs to be a central part of students’ engaging with mathematics of the lesson. Revisions of the first draft occur after course instruction and learning about the Mathematics Teaching Practices (MTPs) (NCTM, 2014).
- MCP-LP Activity 2 - Lesson Plan Module Teacher Candidates' Instructions
- MCP-LP Activity 2 - (Teacher Candidate) Lesson Plan Module Assessment
- MCP-LP Activity 3 - Lesson Planning Module Methods Instructor Instructions
This activity engages the PSMT’s MT in a co-planning, instruction, and observation evaluation of the implemented lesson. This interactive activity provides both the PSMT and MT opportunities to work towards a shared vision of mathematics instruction that results in ambitious and quality mathematics instruction based upon the MCOP2(higher ratings, ambitious teaching).
- MCP-LP Activity 3 - Lesson Planning Module Teacher Candidates’ Instructions
- MCP-LP Activity 3 - (TCs and MTs) Co-Planned MCOP2 Lesson Planning Rubric
- MCP-LPActivity 3 - Lesson Planning Module Mentor Teacher Instructions
- MCP-LP MCOP2 Lesson Planning Rubric
- MCP-LP MCOP2 Observation Protocol
- MCP-LP Post-Lesson Plan Module Survey (TCs & MTs)
- Pre-Lesson Planning Module Background and Beliefs (TCs & MTs)
Standards and Indicators these Materials Target
C.1.2. Demonstrate Mathematical Practices and Processes. SMP Module Activity 2 engages PSMTs in a rich mathematical task where they demonstrate mathematical practices and processes –specifically the SMPs – as they complete the task. They also witness their methods instructor facilitate and intentionally guide the task to elicit their use of SMPs. MCP-LP Module Activity 1 gives PSMTs time to engage with a provided assessment and to engage in the mathematics with the content. PSMTs are encouraged to identify lesson objectives, key concepts, and intentional questions to be posed when presenting their students with the content.
C.2.4. Analyze Teaching Practice. SMP Module Activities 2 and 3 ask PSMTs to analyze the teaching practices of both their methods instructor (Activity 2) and a teacher who implements the task in the exemplar video lesson both individually and collectively as a methods course(Activity 2) and alongside their MT (Activity 3). MCP-LP Module Activity 1 and 2 give PSMTs opportunity to analyze teaching practices through their creation and evaluation of lesson plans. PSMTs are required to create a lesson plan based on a provided assessment (Activity 1) and PSMTs will get feedback from a peer on their lesson plan based on the MCOP2 Lesson planning rubric (Activity 2) and then revise lesson plan to improve design.
C.3.2. Understand & Recognize Students’ Engagement in Mathematical Practices. SMP Module Activities 1, 2, and 3 require PSMTs (and MTs in Activity 3) to investigate and identify student engagement in the SMPs. MCP-LP Module Activity 2 requires PSMTs to evaluate lesson plans using the MCOP2 Lesson planning rubric. The MCOP2 was “designed to measure teacher facilitation and student engagement” examining the SMPs and MTPs comprehensively.
P.1.1. Engage All Partners Productively. SMP Module Activity 3 engages PSMTs and MTs in a conversation around an inquiry-based geometry lesson that specifically includes school-based partners in the work of understanding mathematical practices. MCP-LP Module Activity 3 engages the cooperating mentor teacher with the PSMTs in the lesson planning and self-assessment process. Activity 3 requires that PSTs plan, implement, and reflect on a lesson or quality task (20-45 minutes in length) in a mathematics classroom.
P.3.4. Incorporate Practice-Based Experiences. SMP Module Activity 3 embeds the work of the methods course within the clinical experience to support PSMTs understanding of SMPs beyond the isolation of methods course and into high school classrooms. MCP-LP Module Activity 3 links the work being done in the methods course with the clinical experience to provide PSMTs with a practical experience and feedback on the overall process of teaching.
P.4.1. Collaboratively Develop and Enact Clinical Experiences. SMP Module Activity 3 gathers data from MTs before and after implementation to learn more about their SMP knowledge and needs as well as growth after their experience with Activity 3. Activity 3 helps develop a common language and vision for PSMT development. MCP – LP Module Activity 3 requires that PSMTs collaboratively develop a lesson with their MTs. The PSMTs will then implement the lesson and have their MT observe and rate their instruction using the 16-item MCOP2 Observation Protocol as a formative assessment template. The PSMTs & MTs then participate in a debriefing session following the lesson implementation that provides insight and feedback on the lesson.
P.4.2. Sequence School-Based Experiences. As developed, it is the intention of the comprehensive module development group to allow for sequential implementation – as appropriate for individual program needs –of the SMP and MCP-LP Modules to offer a cohesive and scaffolded development for PSMTs and MTs to engage prior to the student teaching internship semester.
P.4.4. Recruit and Support Qualified Mentor Teachers and Supervisors. SMP Module Activity 3 offers support to MTs as they view and discuss an exemplar video lesson with PSMTs. Part of the intention of Activity 3 is offer examples to MTs for inquiry lessons as well as provide a space for MTs and PSMTs to discuss these practices in the context of their own classrooms. MCP-LP Module Activity 3 provides MTs with an opportunity to review standards based protocols with MTs and to help provide examples and ideas about students’ engagement and teacher facilitation of a particular mathematics lesson.
P.3.5. Provide Effective Mathematics Methods Instructors. The comprehensive module development group offers research-based modules implemented and revised multiple times by multiple programs and instructors to help improve the collective effectiveness of mathematics methods instructors by providing rich, deep, and extensive tasks for PSMTs & MTs. The post-survey allows implementors to offer feedback, modifications and improvements to each module along with a community of methods instructors from which to reflect and both offer and receive support.
About the Authors
Team Leaders & Authors
Jan A. Yow, University of South Carolina, email@example.com
Jeremy Zelkowski, The University of Alabama, firstname.lastname@example.org
Patrice Waller, California State University – Fullerton, email@example.com
Mark Ellis, California State University – Fullerton
Michele Iiams, North Dakota State University
Belinda Edwards, Kennesaw State University
Greg Chamblee, Georgia Southern University
Ivan Cheng, California State University – Northridge
Many Mentor Teachers in secondary mathematics classrooms in partner schools
This work stems from the authors participation in the Mathematics Teacher Education Partnership (Martin & Litchka, 2020) and was partially supported by: Gobstein, H., Strutchens, M, & Sears, R. (2017-21). Collaborative Research: Attaining Excellence in Secondary Mathematics Clinical Experiences with a Lens on Equity. National Science Foundation Improving Undergraduate STEM Education. Grant #s (1726853, 1726998, 1726362).
Koestler, C., Felton-Koestler, M. D., Bieda, K., & Otten, S. (2013). Connecting the NCTM process standards and the CCSSM practices. National Council of Teachers of Mathematics. Martin, W.G., Lawler, B., Litchka, A., & Smith, W. (Eds.). (2020). The Mathematics Teacher EducationPartnership: The power of a Networked Improvement Community to transform secondary mathematics teacher preparation. Information Age Publishing, Inc. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Author. Yow, J. A., Waller, P., & Edwards, B. (2019). A national effort to integrate field experiences into secondary mathematics methods courses. In T. Hodges & A. Baum (Eds.), The Handbook on Research ofField-Based Teacher Education (pp. 395-419). IGI Global. Zelkowski, J., Yow, J., Ellis, M.E., & Waller, P. (2020). Engaging mentor teachers with teacher candidates during methods courses in clinical settings. In Martin, W.G. and Litchka, A. (Eds.). The Mathematics Teacher Education Partnership: The Power of a Networked Improvement Community to Transform Secondary Mathematics Teacher Preparation (pp. 211-234). Information Age Publishing, Inc.