Bridge to the Future The Changing Secondary Mathematics Curriculum

1. Bridge to the FutureThe Changing Secondary Mathematics Curriculum Cheryl Reger, NBCT Neil Reger, NBCT

2. WV’s Next Generation Mathematics Content Standards and Objectives Why do we need yet another set? Sets of state and national math standards have come and gone in the past twenty years. These standards are truly the next generation of standards – the standards are derived from the Mathematics CCSS.

3. WV’s next generation set of standards are written to ensure depth of understanding of the required topics in mathematics. • Provide greater focus and coherence. • Are based on what is known today about how students’ mathematical knowledge, skill, and understanding develop over time. • Focus on the development of mathematical understanding and procedural skills using rich mathematical modeling.

4. Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

5. High School and the Common Core NxG CSOs are organized by conceptual categories, not by courses. Our work has been to group the standards into courses and the courses into pathways. Categories: Number and Quantity Algebra Functions Geometry Modeling Probability and Statistics West Virginia will be using this pathway.

6. What’s Different in High School? Current High School Pathways Algebra I* Geometry Algebra II Conceptual Mathematics Transition Math for Seniors Electives: Algebra III Trigonometry Probability and Statistics Pre-Calculus Calculus AP Calculus AP Statistics Other college level math courses NxGCSOsPathways in West Virginia Math I* Math II Math III(STEM) Math III (LA) Options for the required fourth math credit: Math IV Transition Math for Seniors Advanced Mathematical Modeling STEM Readiness Mathematics Technical Readiness Mathematics AP Calculus AP Computer Science AP Statistics Other college level math courses

7. WV Next Generation Pathway • Common Core Standards are addressed in the three year sequence. • Math I, II, III systematically build proficiency in algebra, geometry, and probability & statistics. • Trigonometry concepts are addressed in Math II & Math III. • Formal Modeling Unit appears in Math III*. • (+) Advanced standards are addressed in Math III STEM.

8. Career and College Readiness A powerful organizing principle of the Next Generation West Virginia State Standards is that of progressions, where an idea is reinforced over grade levels to build depth of understanding. The detailed prescriptions in WVNGMS define the learning progressions and complexity of mathematical content required for career and college readiness in the 21st century.

9. *Fourth and Additional Course Options:

10. High School Math IV The fundamental purpose of Mathematics IV is to generalize and abstract learning accumulated through previous courses and to provide the final springboard to calculus. Students take an extensive look at the relationships among complex numbers, vectors, and matrices. They build on their understanding of functions, analyze rational functions using an intuitive approach to limits and synthesize functions by considering compositions and inverses. Students expand their work with trigonometric functions and their inverses and complete the study of the conic sections begun in Mathematics II. They enhance their understanding of probability by considering probability distributions. Previous experiences with series are augmented. High School Math IV is appropriate for those students that complete Math III STEM.

11. High School STEM Readiness Mathematics This course is designed for students who have completed the Math III (LA) course and subsequently decided they are interested in pursuing a STEM career. It includes standards that would have been covered in Math III (STEM) but not in Math III (LA) (i.e. standards in the CCSS document that are marked with a “+” ), selected topics from the suggested CCSS Math IV course, and topics drawing from standards covered in Math I and Math II as needed for coherence.

12. Advanced Mathematical Modeling Students continue to build upon their algebra and geometry foundations and expand their understanding through further mathematical experiences. The primary focal points of Advanced Mathematical Modeling include the analysis of information using statistical methods and probability, modeling change and mathematical relationships, mathematical decision making in finance, and spatial and geometric modeling for decision-making. Students learn to become critical consumers of the quantitative data that surround them every day, knowledgeable decision makers who use logical reasoning and mathematical thinkers who can use their quantitative skills to solve problems related to a wide range of situations. As they solve problems in various applied situations, they develop critical skills for success in college and careers, including investigation, research, collaboration and both written and oral communication of their work. As students work with these topics, they continually rely on mathematical processes, including problem-solving techniques, appropriate mathematical language and communication skills, connections within and outside mathematics and reasoning. Students also use multiple representations, technology, applications and modeling and numerical fluency in problem-solving contexts.

13. Transition Mathematics for Seniors* Transition Math for Seniors prepares students for their entry-level credit-bearing liberal studies mathematics course at the post-secondary level. This course will solidify their quantitative literacy by enhancing numeracy and problem solving skills as they investigate and use the fundamental concepts of algebra, geometry, and introductory trigonometry. * See current policy for placement criteria.

14. Example Pathway I Students who have completed Technical Readiness II have completed their four courses in mathematics. These students are in the skilled pathway and are interested in entering a technical field upon high school graduation. Should students decide to take courses beyond the CC College and Career Readiness requirements, then Transition Math for Seniors, Advanced Mathematical Modeling and AP Computer Science are appropriate choices.

15. Example Pathway II Students in this pathway, who complete Technical Readiness I and wish to enter college, must take Math III LA or Math III STEM.

16. Example Pathway III Students who wish to enter a non-STEM program of study in college, who have completed their CC College and Career Readiness requirement with Math III LA may then take Transition Math for Seniors, Advanced Mathematical Modeling or College Level Mathematics Courses for their fourth mathematics course.

17. Example Pathway IV Students who decide, after the completion of Math III LA , to change directions and pursue a STEM program at the college level should take STEM Readiness Mathematics or College Level Mathematics courses that would help to prepare them for a STEM program of study.

18. Example Pathway V Students who wish to enter a STEM program of study in college, who have completed their CC College and Career Readiness requirement with Math III STEM would benefit from taking Math IV, AP Calculus, AP Statistics, Calculus or College Level Mathematics Courses. Students who enroll in Calculus or AP Calculus are advised to complete Math IV or College Level Mathematics courses that provide pre-calculus preparation.

19. 8th grade HS Math I Readiness • Options for providing evidence of 8th Grade Mathematics I readiness are: • --Qualifying Exam and/or portfolio for students to demonstrate • Mastery of Math 7 NxG WVCSOs • Mastery of Math 8 NxG WVCSOs not addressed in 8th Grade Mathematics I M.8.NS.1 M.8.NS.2 M.8.EE.1 M.8.EE.2 M.8.EE.3 M.8.EE.4 M.8.EE.5 M.8.EE.6 M.8.EE.7 M.8.G.1 M.8.G.2 M.8.G.3 M.8.G.4 M.8.G.5 M.8.G.9

20. Options for mastering these standards may include: • Before or after school 8th Grade Mathematics I prep time • Summer school opportunities for 8th Grade Mathematics I readiness • Use of suggested Internet resources

21. The Key to Drive Successful Implementation Guide students into the most realistic pathway that includes the courses needed for career and college readiness.