Kindergarten Research Presentation

Brianne Ciarlo

Karly Millar

Amanda Todd

Mathematics | Kindergarten

In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in Kindergarten should be devoted to number than to other topics.

(1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.

S

Operations and Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and

taking from.

Operations and Algebraic Thinking K.OA

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1. Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

3. Decompose numbers less than or equal to 10 into pairs in morethan one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

5. Fluently add and subtract within 5.

Progression documents

Zimba Chart

Progressions for the Common Core State Standards in Mathematics (draft) The Common Core Standards Writing Team

Learning Trajectory from NC State University, College of Education, 29 May 2011

Zimba Chart

A Progression through Kindergarten

-Work within 5-Perceptual to Conceptual Subitizing

-Decomposing to find patterns and generalize for all numbers

-Work within 10-Using level 1 methods and explaining-Show relationships between numbers

-Fluency with adding and subtracting within 5.-Previous knowledge, concrete methods and problem situations enable fluency

Developing Meanings for Addition and Subtraction Encounter problem situations

Level 1 (methods for solving single digit addition/subtraction problems) Using representations for addition and subtraction (fingers, objects, drawings) Concrete methods that foster reflection and discussion

Learning Trajectory for Interpreting CCSS - M

(from NC State University http://turnonccmath.net/index.php)

The Common Core State Standards for Mathematics describe major topics students need to learn in order to reason

proficiently with mathematics, and to be prepared for college and careers........

K.OA.1 - Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out

situations, verbal explanations, expressions, or equations.

http://www.youtube.com/watch?v=M485kQxKnL8

Flexible methods of addition and subtraction include decomposing and composing in many ways

Songs, Finger Play, Verbal Explanations

K.OA.2 - Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to

represent the problem.

http://www.youtube.com/watch?v=0JXMZx-ojxw

Invented StrategiesSplit Strategy (seen in video)

DecomposingJump Strategy

Counting on/Counting backShortcut Strategy

Manipulating numbers so that the calculations are easy

K.OA. 3 - Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and

record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

http://www.youtube.com/watch?v=366cj4x4DNI

Students use counting to attempt to break down numbers into pairs

Using the ten frames and other strategies can help students gain a deeper understanding by guiding them to methods other than counting

K.OA.4 - For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using

objects or drawings, and record the answer with a drawing or equation.

http://www.youtube.com/watch?v=QQzsNDFd7QM

Direct ModelingUsing manipulatives or drawings to represent directly the meaning of the operations

K.OA. 5 - Fluently add and subtract within 5.

http://www.youtube.com/watch?v=kvipSnJeXpo

Students progress towards completing computations mentally so they can do more advanced algebraic functions in later grades.

Student thinking/misconceptions

using but confusing operations

lack of knowledge of inverse relationship between operations

lack of 1:1, cardinality, number sense

missing part-part-whole relationship

difficulty moving from concrete to abstract ideas

not beginning in the right spot on the number line

having difficulty keeping track of ideas due to sloppy or unorganized pictures or use of manipulatives

lack of reading readiness – K.OA.2

Teaching Approaches

Class Discussion

Manipulatives

Modeling

Drawing

Music (Songs/Dance/Fingerplays)

Mini-Lessons

Graphic Organizers

Resources

ixl.com

Van de Walle (Elementary and Middle School Mathematics)

Dr. Lamberg (Whole Class Mathematics Discussions)

Common Core Standards for Mathematics

NCTM

Progression Documents – North Carolina State University, Learning Trajectory, Common Core, Zimba Chart

Assessment

Summative – Cummulative Evaluations End of Unit Tests Standardized Tests

Important for schools and teachers, but they don’t inform teaching decisions

Formative – Along the Way Evaluations that monitor learning Checking for understanding (dipstick) Exit Ticket Anecdotal Record

Provides targeted feedback to the student Results and evidence improve instruction

Bibliography

http://mathdiscussions.wordpress.com/lesson-planning-resources/

Van de Walle, J, Karp, K & Bay-Williams, J. (2010) . Elementary and middle school mathematics: Teaching developmentally (8th edition). New York: Allyn & Bacon.

Lamberg, T. (2012). Whole Class Mathematics Discussions: Improving in-depth Mathematical Thinking and Learning. Boston, MA: Pearson Publishers.

Common Core Standards for Mathematics, 2010

http://www.corestandards.org/assest/CCSI

Lesson 1 – Word ProblemsK.OA.2 (whole class discussion)

Karly has 6 buttons. Brianne gives Karly 4 more buttons. How many buttons does Karly have all together?

Lesson 1 – Word ProblemsK.OA.2 (whole class discussion)

Questions: What do you think went well? What would you change? Why? How was this lesson cognitively demanding? Did the teacher address misconceptions/incorrect solutions? How did the lesson connect to prior knowledge?

Lesson 1 – Word ProblemsK.OA.2 (whole class discussion)

Brianne has 7 buttons. She gave 4 buttons to Karly. How many buttons does Brianne have now?

Lesson 2 – Decompose NumbersK.OA.3 (Button Math)

Lesson 1 offered a Join: Result Unknown problem and Separate: Result Unknown.

After this lesson, we would follow up by offering a Join: Change Unknown Problem. Amanda has 8 buttons. Brianne gave Amanda some more. Now Amanda has 10

buttons. How many did Brianne give her?

According to the progression documents, K.OA.3 directly builds off of the previous standard (covered in Lesson 1)

Lesson 2 (Button Math) Modifications

Gearing Down: Problems anchored to 5 Gearing Up: Taking away the slider