College and Career Readiness Standards-in-Action Professional Development: Mathematical Foundational Units 1-4 (SIA)
This training consists of four units delivered as a daylong training (6 hours plus breaks). The following training units are delivered sequentially.
Foundational Unit 1: Focusing on the Major Work of the Levels (1.5 hours)
This unit will allow participants to investigate in-depth Key Advance 1—focus—within the five adult education levels (A, B, C, D, and E) of the College and Career Readiness (CCR) Standards. At each level, the standards focus on a targeted set of content, and within each level certain content is prioritized. Focus is absolutely critical if instructional time is to be used effectively, efficiently, and productively to prepare students for college and careers. In this training, participants will learn to identify topics that are and are not major topics for the various levels. During the hands-on activity for this unit, participants first will read descriptions that summarize the major work of each CCR adult education level. These descriptions define the most critical concepts and skills for preparing students for college and careers. Then participants will review a set of lesson topics listed by level to determine which of the topics are likely to address the major work of that level. During this activity, small- and whole-group discussions are used to build clear and common understanding among participants of the major work of each level.
Foundational Unit 2: Thinking Across levels to Connect Learning (1.5 hours)
This unit will allow participants to apply what they have learned from Unit 1, during which they explored the importance of focusing on the major work within a level. In this unit, participants will think about linking key mathematical concepts across levels. The activity will provide participants an opportunity to closely read several CCR Standards for Mathematics and then think deeply about how the content progresses across the levels and reflects coherence through their sequencing. Participants will investigate three key progressions present in the CCR Standards: the first dedicated to building fluency with operations, the second dedicated to expressions and equations, and the third focused on real-life applications. Standards within each of the three progressions will be provided to participants on like-colored cards. Participants will be asked to identify which progression (i.e., fluency with operations, expressions and equations, and real-life applications) aligns with each of the three color-coded sets of cards. Then they will organize the cards within each color group by level, from Level A through Level E. By carefully building the learning trajectory within and across levels, participants will learn how the CCR Standards support students’ new understandings based on previously learned concepts and skills.
Foundational Unit 3: Engaging the Three Components of Rigor (1 hour)
This unit prepares participants to relate rigor to the focus concepts of each standard’s level and to the progressions in content across the levels. Participants also learn the importance of the three components of rigor in teaching students to go beyond merely producing correct answers to being able to address and apply mathematical concepts using different perspectives. This unit will allow participants to investigate the three components of rigor. It will teach participants how to recognize each component of rigor from the language of the standards and how to make important connections among these components in instruction. Participants will search selected CCR Standards for clues concerning which of the components of rigor seem to be expected. The goal for participants is to discern the full meaning of each standard. Understanding the demands of a standard will allow them to confirm that the requirements of the standard have been met.
Foundational Unit 4: Connecting Standards for Mathematical Practices (2 hours)
This unit provides participants an opportunity to delve deeply into the Standards for Mathematical Practice and to think about ways in which connections can be made between the Standards for Mathematical Practice and the content of the CCR Standards for Adult Education. In particular, those CCR content standards that set the expectation for “understanding” provide great opportunity for forging these connections and for identifying ways that the Standards for Mathematical Practice can be used to reinforce those areas that merit focus. In this unit, participants will focus on how to integrate the Standards for Mathematical Practice into lessons related to specific content to enrich student learning.