Algebra for All (?)or(!) MASSP Webinar March 4, 2008 Ruth Anne Hodges

Content (?) – What needs to be in place to support Algebra for all (!) – Resources

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

Challenge to Education

1991

What is the mathematics we are requiring of our students? Much of the high school algebra is focused on functions and the interpretation of their graphical representations. –“Technological advances affect what us possible to learn, and what is necessary to learn” (High School Mathematics Content Expectations, pg.2)

David Eggenschwiler, an English professor emeritus at USC, writing in the LA Times, Jan 5, “…let us not hear repeatedly that high school algebra is a waste of time because it does not directly train students for the job market....It teaches the mind how to think… Let us instead ask the harder question: How can we better prepare students to study algebra? It would surely not be easy, but it is worth doing.”

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

Algebra I and II courses: 3 parts – 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)

Algebra I and II courses? 3 parts (cont) Statistics –Bivariate date – Algebra I 2 variables – usually change over time such as mph or stock prices. Extends work with functions, especially linear functions –Univariate data and probability - Algebra II One variable – i.e. MEAP results, sports scores builds on the work done in middle school (i.e. bar graphs, normal curve) and applied in social studies and science Information needed for a data-driven world and to be knowledgeable citizens

Mathematical Proficiencies A mathematically proficient student has conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and a productive disposition.

Instruction For students to be mathematically proficient with the required content, instruction needs to incorporate the Teaching and Learning Standards: higher-order thinking deep knowledge substantive conversation connections beyond the classroom

Instruction “Effective implementation of the Standards for Teaching and Learning assumes that the classroom context is predicated on the belief that all students can and will learn. In order to be successful, instruction must not only incorporate the standards listed above, but it must also take place within an environment that provides sufficient social support to permit all students to learn no matter what their gender, ethnicity, socioeconomic status, disability, English language proficiency, or preferred learning style”. Michigan Curriculum Framework, 1996

How do we determine proficiency? With credit based on proficiency, student achievement shouldn’t be measured against others.

What does it mean to be proficient? But instead they should be measured against a continuum of progress.

A Continuum of Assessment Information very discrete diagnostic “the trees” very “gross” summative “the forest” Item AnalysisProficiency Level ?

What About This Middle Area? This area is where “standards-based” information fits in Standards-based information –is not as discrete as specific misconceptions –Is compact enough to be useful instructionally Standards are likely the level at which we want to “credential” our students

The End Results…

Summary Provide a coherent curriculum, incorporating technology wherever possible Consider an integrated approach to mathematics instruction, including incorporating into science, social studies and CTE programs where possible Use the 4 th mathematics credit to provide supports for struggling students Use formative assessment and unit assessments for measures of proficiency Encourage and support good instruction based on the Teaching and Learning Standards

National Council of Teachers of Mathematics

National Association for Secondary School Principals

ASCD

Resources MDE Mathematics Page MDE High School Page Mathematics HSCE Clarification Michigan Council of Teachers of Mathematics Math/Science Center Network Secondary Credit Assessment System > Secondary Credit Assessment System