Western Oregon University's Middle School Mathematics Focus Laurie Burton, Maria Fung & Klay Kruczek MAA Session on Content Courses for the Mathematical Education of Middle School Teachers Friday January 5, 2007

Preservice Teacher Mathematics Program First Shared foundational coursework for all future K - 8 teachers 15 quarter credits

Core first year sequence Mathematics for Elementary and Middle School Teachers Number Sense; Rational Numbers, Probability and Statistics and Geometry Lab-based, hands on and focused on active learning

(Shared by K-8) Advanced coursework Problem Solving for Teachers Write, solve and assess rich word problems Mentor children via the Math Forum

Our Middle School Mathematics Focus After the shared foundational coursework, future Middle School Mathematics teachers take: Four advanced courses as well as Geometry for MS teachers and Calculus for MS Teachers (Two years of coursework)

Four Advanced MS Courses Four courses from Manipulatives in Mathematics College Algebra for teachers Probability Statistics for teachers Integrated Methods for teachers Abstract Algebra for MS teachers

Manipulatives in Mathematics Materials Department coursepack Base pieces, tiles, pattern blocks, Cuisenaire rods, Fraction Bars, Decimal Squares, paper-folding, geoboards

Manipulatives in Mathematics Content Whole Number operations Fraction operations Decimal operations

Manipulatives in Mathematics Pedagogy Manipulative-based hands-on activities Lesson Plan research and presentations

College Algebra for Teachers Materials Visual Algebra Coursepack Black and Red Tiles Algebra Pieces

College Algebra for Teachers Content Integer operations Modeling sequences of tile figures Algebraic Expressions Linear and Quadratic Equations

College Algebra for Teachers Pedagogy Visual-manipulative based Verbal, Numerical and Symbolic methods are all explored

Probability and Statistics for Teachers Materials Workshop Statistics Fathom

Probability and Statistics for Teachers Content Data collection Representation and analysis Experimental simulation and sampling

Probability and Statistics for Teachers Pedagogy Hands-on activities Games Computer based simulations

Integrated Methods for Teachers Materials Elementary and Middle School Mathematics, Teaching Developmentally (Van de Walle)

Integrated Methods for Teachers Content Early Number Concepts Whole Number Operations Place Value Ratio and Proportion Measurement

Integrated Methods for Teachers Pedagogy Writing reflective essays, activities and lesson plans Integrating appropriate content with best-practice pedagogy

Abstract Algebra for Middle School Teachers Materials Department coursepack Colored pencils

Abstract Algebra for Middle School Teachers Content Number Systems (advanced) Elementary Group Theory Cayley tables and Cayley table art Basic Cryptography

Abstract Algebra for Middle School Teachers Pedagogy Exploration and discovery of abstract concepts

GEOMETRY FOR MIDDLE SCHOOL TEACHERS Required course for future middle school mathematics teachers

Geometry for Middle School Teachers Materials Department coursepack— including Math and the Mind’s Eye materials and Portland State University materials The Geometer’s Sketchpad

Geometry for Middle School Teachers Content Straight-edge and compass constructions Plane Isometries (construction, composition and equivalence)

Geometry for Middle School Teachers Content Tessellations Dilations Area Pythagorean Theorem Special Triangles

Geometry for Middle School Teachers Pedagogy Hands-on group activities Exploratory computer labs

Geometry for Middle School Teachers Sample Activity Students construct regular and non-regular polygons on the sides of right triangles to discover the Pythagorean Theorem still works when regular polygons are placed on each side of a right triangle

Geometry for Middle School Teachers Sample Activity Students discover the Pythagorean Theorem does not work for acute and obtuse triangles

Geometry for Middle School Teachers Sample GSP Activity Students discover how to tessellate the plane with an arbitrary quadrilateral using several isometries

Geometry for Middle School Teachers Sample GSP Activity Students refine their approach to discover that only one isometry (rotation) is actually required

CALCULUS FOR MIDDLE SCHOOL TEACHERS Required course for future middle school mathematics teachers

Calculus for Middle School Teachers Materials Department coursepack— including Math and the Mind’s Eye materials and Portland State University materials Graphing calculator

Calculus for Middle School Teachers Content Derivatives and Integrals of polynomial functions in an applied context Optimization Velocity and Acceleration

Calculus for Middle School Teachers Pedagogy Exploration-based Hands-on, intuitive and graphical methods used

Calculus for Middle School Teachers Sample Activity Students construct all possible open-top boxes with integer heights out of 20 x 25 grid paper. Students use the physical models to arrange the boxes in terms of increasing volume

Calculus for Middle School Teachers Sample Activity Students compute the actual volume of the boxes and compare these results to their predictions

Calculus for Middle School Teachers Sample Activity Students graph the volume of the boxes as a function of height and use this graphical representation to determine the symbolic volume function

Calculus for Middle School Teachers Sample Activity Students determine the average rate of the change of volume with respect to height and relate this to the behavior of the graph of the volume function