Meeting the CORE Through Connections to the Arts

Presented at Tennessee Mathematics Teachers

State ConferenceMemphis University School

Memphis, TennesseeSeptember 28, 2013

Ann AssadAustin Peay State University

Clarksville, Tennessee

Amy AssadDogwood Elementary School

Germantown, Tennessee

Numeracy – The capacity for quantitative thought and expression

• Practical numeracy – applications to daily life • Civic numeracy – ability to draw inferences from

data related to issues that benefit society• Professional numeracy – computational and

analytical skills related to the workplace• Numeracy for leisure and cultural numeracy –

understanding of the role of mathematics in games, puzzles, art, music, and dance

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

-- G. H. Hardy, Number Theorist

Integrating the teaching of mathematics and the arts--• Increases student motivation and engagement• Addresses multiple intelligences and learning

styles• Provides opportunities for differentiated

instruction• Honors cultural and ethnic diversity• Provides multiple opportunities for assessment• Connects mathematics, science, social studies

and language arts in meaningful contexts.

Common Core Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning

of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Geometry K.G.Identify and describe shapes (squares, circles, triangles, rectangles,hexagons, cubes, cones, cylinders, and spheres).1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.2. Correctly name shapes regardless of their orientations or overall size.3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three dimensional (“solid”).

A kindergarten teacher observed that her students struggled to describe objects to other classmates. Instead of using language, they pointed or moved objects. She worked with the art teacher to create an activity that would require them to work with vocabulary related to shape and position.

The class read The Shape of Things by Dayle Ann Dodd.

Put pictures from book here

The art teacher created the following rendition of a parade scene.

Student comments indicate students’ understanding of mathematical language and some misconceptions.

Nadia: I see a ladder and an alarm. The ladder is two thin and long rectangles and a few short ones across.Timmy: Up there is a plane holding a flag with words on it.Teacher: Where is the plane?Timmy: Uphill, in the air.Teacher: Where is the banner?Manuella: It’s in the back of the plane.Beverly: No, it behind the plane.Nathan: That’s the same thing. Beverly: No, it’s not.Manuella: Yes, it is.

Beverly: In the back isn’t behind. The flag is behind the plane because it is pulled. It’s not in the back of the plane.Caleb: I see a dog.Beverly: He’s in the middle of the clown and the fire engine.Nadia: There is a circle in the center of the propeller.Beverly: The flag that the plane is pulling is a rectangle.Alyssa: It’s kind of like a rectangle, but it curvy.Nathan: The wheels on the fire engine are funny. One has a triangle and the other kind of does.Beverly: They are arrows: one pointing up. The other is point this way. (Beverly points her finger to the left.)

---- From Show and Tell: Representing and Communicating Mathematical Ideas in K-2 Classrooms

Operations and Algebraic Thinking K.OA

Understand addition as putting together and adding to, and understandsubtraction as taking apart and taking from.1. Represent addition and subtraction with objects, fingers, mentalimages, drawings, sounds (e.g., claps), acting out situations, verbalexplanations, expressions, or equations.

Understand and apply properties of operations and the relationshipbetween addition and subtraction.3. Apply properties of operations as strategies to add and subtract.3 Examples:If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property ofaddition.) To add 2 + 6 + 4, the second two numbers can be added to makea ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Music and the Fact Families

http://farmingtones.scsk12.org/~sbenzing/Site/Welcome_to_2nd_grade!.html

Working with Addition and Subtraction

• Kindergarten: Understand addition, and understand subtraction.

• Grades 1 and 2: Represent and solve problems involving addition and subtraction.

• Grades 1: Understand and apply properties of operations and the relationship between addition and subtraction.

• Grades 1 and 2: Add and subtract within 20.• Grade 1: Work with addition and subtraction

equations.

Way up high in the apple treeTwo* red apples smiled at me

I shook that tree as hard as I could(pause) Down came the apples –

mmm, they were good!

Multiplication and Division

• Grade 2: Work with equal groups of objects to gain foundations for multiplication.

• Grade 3: Represent and solve problems involving multiplication and

• Grade 3: Understand properties of multiplication and the relationship between multiplication and division.

• Grade 3: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

• Grade 4: Use the four operations with whole numbers to solve problems.

• Grade 4: Gain familiarity with factors and multiples.

• Grade 4: Generate and analyze patterns.• Grade 5: Analyze patterns and relationships.

A Section

Rondo

Fractions

• Grade 3: Develop understanding of fractions.• Grade 4: Extend understanding of fraction

equivalence and ordering. • Grade 4: Build fractions from unit fractions.• Grade 5: Use equivalent fractions as a

strategy to add and subtract fractions.

This student was asked to show what ¾ means in as many ways as possible.

Music Note Values

Whole Note – Four Beats

Half Note – Two Beats

Quarter Note – One Beat

Eighth Note – One Half Quarter Note

Sixteenth Note – One Fourth Quarter Note

Geometry, Measurement, and Spatial Relationships

Geometry, Decimals and Money, Problem Solving

My Design

References and Resources• The Shape of Things by Dayle Ann Dodds, Julie Lacome

(Illustrator). ISBN-13: 9781564026989• The Shape of Things video (YouTube – Sound quality is not good.)

http://www.youtube.com/watch?v=1h1HcChju_0• Show and Tell: Representing and Communicating Mathematical

Ideas in K-2 Classrooms by Linda Dacey an Rebeka Eston. ISBN-13: 978-0-941355-50-6

• Online T-Shirt Company: http://www.ooshirts.com/• Common Core State Standards Initiative:

http://www.corestandards.org/• Reconceptualizing Mathematics for Elementary School Teachers,

2nd Edition by Judith Sowder, Larry Sowder, and Susan Nickerson. ISBN-13: 978-1464103353

All too often schools teach mathematics primarily as a set of skills needed to earn a living, not as a general approach to understanding patterns and solving problems.The disconnection of mathematical study from other school subjects--from history and sports, from language, and even from science--is one of the major impediments to numeracy in today's schools. -- Lynn Arthur Steen