Providing ALL Students

1. Providing ALL Students A 21st Century Mathematics Education

2. Competencies for High School Completion Core Academic Environment for Delivery Policy needed for Reform Content Standards Mathematics English Science Social Studies CTE Integrated Instructional Design & Delivery Intervention/Support Programs Infrastructure School Redesign Policy-making State Board Legislature Districts Incentives Requirements Postsecondary

3. So how do we create an environment for delivering a 21st century mathematics education for students?

4. Agenda • Content • Instruction • Assessment • Organization of content and instruction, or Is a PC necessary?

5. Content • The Michigan Merit Curriculum requirements for the first time provide: • Michigan schools with a common set of graduation requirements and • Teachers a common set of learning expectations. • A diploma means students learned the content required by the MMC.

6. Content • The mathematics HSCE=3 credits • Legislation says students need 4 mathematics credits not Algebra I &II, and Geometry credit • Credit is based on demonstrated proficiency with the content • Not seat time or course

7. 1992 Content

8. So what is algebra? Content • Algebra has 2 components: • Algebra: the manipulation of symbols; rules to be remembered – transformational algebra • Algebraic Reasoning: a systemic way of expressing generality and abstraction – representational algebra From Adding it Up – pg 256

9. Algebra Content of the HSCE Content Functions – representational algebra • “interpret the symbolic form and recognize the graph” (A2) • Mathematical modeling: what is the function telling us about the real-world?(A2) • Understand the big ideas of functions (A2) by studying the various function families(A3) Calculations – transformational algebra • Less than 15% of the expectations in Algebra I and less then 25% of the expectations in Algebra II are purely calculations (A1) • often very specific (small grain size)

10. Content • “Technological advances affect what us possible to learn, and what is necessary to learn” (High School Mathematics Content Expectations, pg.2)

11. Instruction

12. Instruction • Technology is essential for all students to learn the HSCE

13. Instruction • Research has shown that the teacher has the most effect on student learning and that “content knowledge is crucial to teaching effectiveness”. • According to Deborah Ball (U of M; National Mathematics Advisory Panel) there is a mathematical knowledge needed for teaching that is in some ways more complex than just knowing the mathematics. Teachers need to have a “mathematical eye” as well as a “pedagogical eye”. (http://www-personal.umich.edu/~dball/presentations/032408_AERA.pdf)

14. Instruction What We Can Do About Achievement Disparities • “If we are truly committed to equitable outcomes, then we must commit more resources to those students who most need them” including: • Good teachers • Rich mathematics curriculums

15. Instruction Nine Ways to Catch Kids Up • Strategies essential to successful intervention instruction include: • Determine and scaffold the essential mathematics content • Pace lessons carefully • Build in a routine of support • Foster student interaction

16. Instruction Effective Strategies for Teaching Students with Difficulties in Mathematics http://www.nctm.org/uploadedFiles/Research_Issues_and_News/Briefs_and_Clips/brief_students_difficulties.pdf

17. Assessment

18. Assessment • Standards based assessment • Organizing information in grading records by learning goals (A Repair Kit for Grading: 15 Fixes for Broken Grades, ETS) • Formative assessment • Assessment for learning

19. Assessment NCTM

20. The End Results… Assessment james.gullen@oakland.k12.mi.us

21. The End Results… How to avoid a PC • Use the 4th credit, i.e. • Algebra II over 2 years for 1 credit with enough extra math embedded to make up the 4th credit • Algebra II for 2 years for 1 credit alongside a CTE program that has math-related content • Integrated sequence of required HSCE plus enough extra mathematics to = 4 credits • Pull out the statistics from Algebra I &II, and design a statistics class that incorporates enough extra statistics work to equal another credit • Provide a support class/math lab where struggling students can go for help

22. Intervention Lenses • Learning Significant Mathematics—What guarantees the learning of every student? What provides the mathematical power that every student should expect? • Knowing the Mathematics—How do we know that the providers know the mathematics and the appropriate pedagogy that ensures understanding is developed by every student? • Assessment and Data Gathering—How do we know the understanding that every student brings to the situation? What information determines the goal setting? • Quality Planning and Delivery—Is the planning and delivery transparent? Are they flexible enough to address the needs of every student? • Alignment—What structures are in place to align the services chronologically? How is curricular alignment ensured? How have pedagogical strategies been addressed and aligned with content and needs? How are appropriate standards and goals aligned with the delivery of services for every student? by Nancy Berkas and Cynthia Pattison (NCTM News Bulletin, September 2007) http://www.nctm.org/2007_09nb_intervention.aspx

23. School Practice Differences Between Average/High Impact Schools

24. Recommendations • Provide a coherent curriculum, incorporating technology wherever appropriate and possible • Encourage and support good instruction based on the Teaching and Learning Standards, including providing professional learning opportunities for teachers • Consider an integrated approach to mathematics instruction, including incorporating into science, social studies and CTE programs where possible • Use formative assessment and standards-based grading systems for measures of proficiency • Use the 4th mathematics credit to provide supports for struggling students

25. Resources • National Council of Teachers of Mathematics (www.nctm.org) • Journal articles, intervention section, research briefs • Michigan Council of Teachers of Mathematics (www.mictm.org) • Annual summer institute and conference • ASCD (www.ascd.org) • November 2007 issue • Michigan Mathematics/Science Centers ( www.mscenters.org ) • professional development; materials and resources for mathematics teaching • Texas Instruments • www.education.ti.com • Educational Testing Service • www.ets.org

26. Contact Information Ruth Anne Hodges hodgesr3@michigan.gov www.michigan.gov/mathematics www.mdepersonalcurriculum.wikispaces.com