What Do Magnets Have to Do with Geometry and Developing Geometric Vocabulary?

Transcription

1 What Do Magnets Have to Do with Geometry and Developing Geometric Vocabulary? Eric Shippee College of William and Mary Marguerite Mason College of William and Mary Robert L. Provost Jr. King and Queen County Public Schools

2 NCTM Focal Points According to Curriculum Focal Points for PreKindergarten through Grade 8 Mathematics (NCTM, 2006, p. 37) In grades 6-8 students should: Precisely describe, classify, and understand relationships among types of two- and threedimensional objects using their defining properties Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

3 The van Hiele Levels of Geometric Understanding Level 0: Pre-recognition. Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided polygons. Level 1: Visualization. Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between components of the figure. A student should recognize & name figures and distinguish a given figure from others that look somewhat the same.

4 The van Hiele Levels of Geometric Understanding Level 2: Analysis. Properties are perceived, but are isolated and unrelated. A student should recognize and name properties of geometric figures. Level 3: Abstraction. Definitions are meaningful, with relationships being perceived between properties and between figures. Logical implications and class inclusions are understood, but the role and significance of deduction is not understood.

5 The van Hiele Levels of Geometric Understanding Level 4: Deduction. The student can construct proofs, understand the role of axioms and definitions, and know the meaning of necessary and sufficient conditions. A student should be able to supply reasons for steps in a proof. Level 5: Rigor. The standards of rigor and abstraction represented by modern geometries characterize level 5. Students can manipulate symbols without referents according to the laws of formal logic. A student should understand the role and necessity of indirect proof and proof by contrapositive.

6 Assessment Results by Subgroup Mathematics Grades Adv Prof Pass Adv Prof Pass Adv Prof Pass STATE All SPED K&Q All SPED < < < < < < STATE All SPED K&Q All SPED 7 < < < < < < STATE All SPED K & Q All SPED < < < 0 8 8

7 The Importance of Vocabulary TIDEWATER TEAM WEBSITE

8 Our intervention Building vocabulary through the use of magnetic manipulatives

9 Point Definition: A point can not be defined. It is described as an exact location. It has no dimension.

10 Line Definition: Line has no definition. It is described as a set of points that goes on and on in both directions. A line has no end points. It has one dimension.

11 Line Segment Definition: Part of a line; a line segment has two end points.

12 Ray Definition: Part of a line that starts at a point (the end point) and continues forever in one direction.

13 Angle Definition: A geometric figure formed by two rays called sides having a common endpoint called the vertex.

14 Refining the Student Definitions In depth look at side length and angles for Rhombus and Square. For rectangles focus on right angles, not side length.

15 Square VS Rhombus A square is a quadrilateral with four congruent sides and four right angles. A rhombus is a quadrilateral with four congruent sides.

16 Square VS Rectangle A square is a quadrilateral with four congruent sides and four right angles. A rectangle is a quadrilateral with four right angles.

17 Parallelogram Definition: A quadrilateral with both pairs of opposite sides parallel. Properties: opposite sides congruent opposite angles congruent diagonals bisect each other

18 Other Angle Manipulatives

19 Cube Students will observe that a cube is made up of six distinct square faces and eight vertices.

20 Prism A polyhedron with two parallel congruent polygonal bases, and all lateral faces are parallelograms.

21 Nets

22 Conclusion Magnetic manipulatives are an effective tool that allow students to develop the ability to: Precisely describe, classify, and understand relationships among types of two- and threedimensional objects using their defining properties Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

23 Sources National Council Teachers of Mathematics (NCTM). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. Reston, VA: NCTM, VADOE: report.do?division=49&schoolname=all

24 Sources Magnetix: this item is no longer being produced but can be purchased through E-Bay. Other manufactures do produce similar items. Anglegs and angle rulers from ETA Cuisenaire: Magformers:

25 Contact Information The power point is available on our website Eric Shippee: Marguerite Mason: Robert L. Provost Jr. Thank you and have a great day!