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A A 21st Century 21st Century Mathematics Mathematics Education Education Providing ALL Students Providing ALL Students
A A 21st Century 21st Century
MathematicsMathematics Education Education
Providing ALL StudentsProviding ALL Students
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Competenciesfor High School Completion
Core Academic
Environment for Delivery
Policy needed for Reform
Content Standards
MathematicsEnglishScience
Social Studies
CTE Integrated
Instructional Design & Delivery
Intervention/Support Programs
Infrastructure
School Redesign
Policy-making
State BoardLegislature
Districts
IncentivesRequirementsPostsecondary
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So how do we create an environment for delivering a 21st century mathematics education for students?
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AgendaAgenda
Content Instruction Assessment Organization of content and
instruction, or Is a PC necessary?
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ContentContent 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.
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ContentContent 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
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19921992ContentContent
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So what is algebra?So what is algebra? 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
ContentContent
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Algebra Content of the HSCEAlgebra Content of the HSCEFunctions – 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)
ContentContent
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– “Technological advances affect what us possible to learn, and what is necessary to learn” (High School Mathematics Content Expectations, pg.2)
ContentContent
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InstructionInstruction
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•Technology is essential for all students to learn the HSCE
InstructionInstruction
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• 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)
InstructionInstruction
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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
InstructionInstruction
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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
InstructionInstruction
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InstructionInstruction 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
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AssessmentAssessment
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AssessmentAssessment
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
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AssessmentAssessment
NCTM
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The End Results…The End Results…How to avoid a PCHow 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
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Intervention LensesIntervention 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
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School Practice Differences Between School Practice Differences Between Average/High Impact SchoolsAverage/High Impact Schools
High Impact Focus on Post Secondary Goals
Academic Driven
Embrace Standards and Assessment
High expectations for all students
Encourage Academic Challenge
Data used for curriculum improvement
Help prepare students for college requirements
Early warning systems
Counselors members of academic team
Teacher assignment based on student needs and teacher
expertise
Average Impact Focus on Graduation
Rules Driven
Tolerate Standards and Assessment
High Expectations for selected students
Barriers to challenging courses
Data used to measure past student performance
Delay entry into grade level courses
Remedial help after students falter
Counselors involved through referrals
Teacher assignment based on seniority and preference
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RecommendationsRecommendations 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
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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
ResourcesResources
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Contact InformationContact Information
Ruth Anne [email protected]
www.michigan.gov/mathematics
www.mdepersonalcurriculum.wikispaces.com
