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Carroll Math Seminar

Teaching Math is Teaching Thinking

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Teaching Math is Teaching Thinking

• For children with language-based learning difficulties (LBLD), math is often as difficult to master as reading. While a great deal of research and curriculum development has occurred in reading instruction for these students, very little has been accomplished in the world of math learning for children with LBLD.

http://carrollmath.ning.com/

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Back Ground• The Carroll School math department decided to develop an approach for teaching math to student with learning differences. The approach relies on five central foundations:

(1) Cognitive Development, (2) Problem Solving,(3) Communication, (4) Discovery, and

(5) Applications to traditional math.http://www.carrollschool.org/documents/educators/MathSeminar-July2009.pdf

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David Stevens Comments

• The United States teaches almost every math topic in every grade, teaching and re-teaching a little bit on each topic.

• Other countries focus on teaching fewer topics per grade than the United States, going more in depth and ensuring greater understanding of the topics.

• This approach is the reason why teachers feel so pressured to keep moving through curriculum, especially with the standardized testing that is used so much in our country.

• Many of our international counterparts do not even use standardized testing

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What are some of the holes in our student’s

learning?

• Multi-step problem solving• Working memory affects work on a

whole• Place value• Number sense 4 =• Different levels of cognitive skills in the

class• David Stevens, Cognitive Psychologist

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Number Sense

• Number sense is to MATH what Phonemic Awareness is to Reading Acquisition

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Math Wars

A battle between the Progressive Approach and

Traditional Approach towards teaching math

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Carroll Math

• Carroll Math is currently a mix of several math programs that work well with children with learning difficulties.– Cognitive Activities– Symphony Math Program– Singapore Math– Stern Math– Number Worlds– Tom Harding Math

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Cognitive ActivitiesMath classes start with cognitive activities.The Carroll School uses 5 activities (used 1 at a time) through out the year. These activities are use as a warm up to promote thinking skills.

1. What's My Rule?2. Pattern and Sequences 3. Attribute Chain Activity4. Matrix Activity5. Mastermind

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Activity Language

• Terms used “I agree” & “I disagree”

• These terms are used instead of “correct or right” and “incorrect or wrong”.

• These terms help promote a more positive atmosphere.

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What’s My Rule?

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• \\Server-hank\Faculty Work Share\DeMichael\WMR 2 Circles.galleryitem

• \\Server-hank\Faculty Work Share\DeMichael\WMR 3 Circles.galleryitem

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Patterns Activity– Supplies:

• Set of colored blocks with up to 6 colors– Creating Patterns:

• The leader of the activity decides on a pattern ahead of time. For young children who are leading it may be good to draw a picture on a card to use as a reference to begin.

• Put out a couple components of the pattern. The children then choose one piece at a time to try to complete the pattern.

• The leader responds to each piece with “I agree” or “I disagree.”

• The goal being for the children will be able to name the pattern being illustrated.

• Eventually ask the children to build the pattern in multiple directions

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Patterns Activity

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0011 0010 1010 1101 0001 0100 1011• Supplies:

- Attribute Block• Chain Game (Linear Attribute Game, multiple

players) place the attribute pieces in the center of the table. The teacher decides how many attributes to change between each piece in the chain, starting with one difference between each shape. Play begins when one player selects a piece from the attribute blocks and places it on the table. The second player selects a piece which differs from the first one by the previously agreed number of attributes.

Attribute Chaining Activity

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• Continue in this manner until all the shapes are used. To play this game competitively, give each player the same number of shapes. The first player to use all their shapes wins. You can play this game with one, two, three, or four attribute changes between each shape. When the students can work thought the activity at each level efficiently move to the matrix activity.

Color Shape Size Color

Attribute Chaining Activity

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Matrix Activity

• Chain Activity Two Dimensional Game (2D Attribute Game, multiple players) This is an extension of the Attribute Chaining Activity. First, place the attribute pieces in the center of the table. When starting this activity the teacher often chooses a number of attributes to change by vertically and horizontally (see completed matrix example below).

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Matrix Activity

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Matrix Activity

When starting out children can struggle to complete this activity because they do not have a plan or an organization to their matrix. Over time they begin to strategize as they build by choosing what attributes to change ahead of time.

 

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Mastermind• A popular thinking game• A peg & board game can be commercially

bought but Carroll uses colored blocks so it is easier to differentiate instruction

• Carroll spends 10-15 minutes to play this game in class

• Supplies: Set of colored blocks with up to 6 colors

• Language of the game: - Agree – Correct color in the correct location- Partially Agree – Correct color but incorrect

location- Disagree – That color is not in the pattern

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Mastermind• One player hides two blocks behind a shield

in a specific order (2 is a good starting point, can increase number of blocks as children need more challenge)

• The other players try a two block combination and get the hider’s response to the attempt

• The players should use the responses from each attempt to reason out their next move and finally the answer

• We hope that kids can hold the responses in their mind, but if they cannot it is OK to use a notation system

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Visual Overview of the Mastermind Game: Notation System: =Disagree =Partially Agree =Agree 

Hidden Goal: Notation of Progress_____________________________________________________________

Start:

 Win!

Mastermind

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Symphony Math• Computer/Web based math program, created and updated by David Stevens• Goal is to have students use the program for a minimum of 45 minutes each week, 2 times in school and 2 times for homework.• Symphony is designed to find where the gaps are in a child’s thinking and address them on an individual basis. • Focuses on giving children a solid foundation of math

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Symphony Math• Program starts with number sense and goes

through 17 stages. It is designed like a road map of mathematical development.

• The number sense section attaches the symbols of numbers to quantity.

• The program has the ability to read word problems aloud, restate the directions and give help. If a student over uses the help button the program will turn the help button off.

• To play with the program you can go to…owww.symphonylearning.com

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Singapore Math

• In the U.S., the term “Singapore Math” often refers to a collection of math teaching strategies common in Singaporean classrooms. Sometimes it describes the full math curriculum used in Singapore for grades K–6. Singapore Math emphasizes the development of strong number sense, excellent mental-math skills, and a deep understanding of place value.

• The curriculum is based on a progression from concrete experience—using manipulatives—to a pictorial stage and finally to the abstract level or algorithm. This sequence gives students a solid understanding of basic mathematical concepts and relationships before they start working at the abstract level.

http://www.sde.com/singapore%2Dmath

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Singapore Math• The Singapore approach focuses on developing

students who are problem solvers. It includes a strong emphasis on model drawing, a visual approach to solving word problems that helps students organize information and solve problems in a step-by-step manner.

• Concepts are taught to mastery, then later revisited but not re-taught. It is said the U.S. curriculum is a mile wide and an inch deep, whereas Singapore’s math curriculum is said to be just the opposite.

http://www.sde.com/singapore%2Dmath/

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Stern Math

• Is a multisensory, manipulative-based, conceptual Approach to Teaching Mathematics

• http://www.sternmath.com/description.html

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Number Worlds The Number Worlds curriculum, developed by Sharon

Griffin, teaches the specific math concepts and skills that are the foundation for later mathematical learning. It also exposes students in grades PreK-6 to the many different ways that number and quantity is represented and talked about, so children can use the number knowledge they acquire flexibly, across contexts. The Number Worlds program has been extensively evaluated with children from low-income populations and proven effective in enhancing computational fluency, number sense, mathematical reasoning and communication, as well as performance on standardized mathematics achievement tests

http://clarku.edu/numberworlds/NWGenProgDesc.htm

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National Library of Virtual Manipulatives

• http://nlvm.usu.edu/en/nav/vLibrary.html