The document provides background information on tangrams, including: - Tangrams originated in China as furniture pieces that people later used as puzzles by forming shapes with 7 wooden blocks. - They were introduced to the Western world in the early 1800s and became popular. - Mathematicians later proved there are only 13 possible convex shapes that can be formed with the 7 pieces. - Traditional tangrams used materials like stone, bone or wood, while modern sets often use plastic.

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Peer Tutoring...
a proactive intervention for the classroom
Introduction:
Peer tutoring is an organized learning experience in which one student serves as the teacher or
tutor, and one is the learner or tutee. It gives students an opportunity to use their knowledge in a
meaningful, social experience .Tutors reinforce their own learning by reviewing and reformulating
their knowledge. Tutees gain one-on-one attention. Both tutors and tutees gain self-confidence
(Howard et al., 1986), the tutor by seeing self- competence in his or her ability to help someone and
the tutee by receiving positive reinforcement from peers.
WHAT IS PEER TUTORING?
Peer tutoring is a flexible, peer-mediated strategy that involves students serving as academic tutors
and tutees. Typically, a higher performing student is paired with a lower performing student to
review critical academic or behavioral concepts.
WHY CHOOSE PEER TUTORING?
 It is a widely-researched practice across ages, grade levels, and subject areas
 The intervention allows students to receive one-to-one assistance
 Students have increased opportunities to respond in smaller groups
 It promotes academic and social development for both the tutor and tutee
 Student engagement and time on task increases
 Peer tutoring increases self-confidence and self-efficacy .
 The strategy is supported by a strong research base .

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WHAT ARE THE MOST FREQUENTLY USED PEER TUTORING MODELS?
Classwide Peer Tutoring (CWPT): Classwide peer tutoring involves dividing the entire class into
groups of two to five students with differing ability levels. Students then act as tutors, tutees, or
both tutors and tutees. Typically, CWPT involves highly structured procedures, direct rehearsal,
competitive teams, and posting of scores The entire class participates in structured peer tutoring
activities two or more times per week for approximately 30 minutes. While the procedures and
routines in CWPT remain the same, student pairings or groups may change weekly or biweekly. In
CWPT, student pairings are fluid and may be based on achievement levels or student compatibility.
Students may
Cross-age Peer Tutoring: Older students are paired with younger students to teach or review a
skill. The positions of tutor and tutee do not change. The older student serves as the tutor and the
younger student is the tutee. The older student and younger student can have similar or differing
skill levels, with the relationship being one of a cooperative or expert interaction. Tutors serve to
model appropriate behavior, ask questions, and encourage better study habits. This arrangement is
also beneficial for students with disabilities as they may serve as tutors for younger students.
Peer Assisted Learning Strategies (PALS): PALS, a version of the CWPT model, involves a
teacher pairing students who need additional instruction or help with a peer who can assist. Groups
are flexible and change often across a variety of subject areas or skills. Cue cards, small pieces of
cardstock upon which are printed a list of tutoring steps, may be provided to help students
remember PALS steps .All students have the opportunity to function as a tutor or tutee at differing
times. Students are typically paired with other students who are at the same skill level, without a
large discrepancy between abilities.
Reciprocal Peer Tutoring (RPT): Two or more students alternate between acting as the tutor and
tutee during each session, with equitable time in each role. Often, higher performing students are
paired with lower performing students. RPT utilizes a structured format that encourages teaching
material, monitoring answers, and evaluating and encouraging peers. Both group and individual
rewards may be earned to motivate and maximize learning. Students in RPT may prepare the
instructional materials and are responsible for monitoring and evaluating their peers once they have
selected a goal and reward as outlined by their teacher.

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Same-age Peer Tutoring: Peers who are within one or two years of age are paired to review key
concepts. Students may have similar ability levels or a more advanced student can be paired with a
less advanced student. Students who have similar abilities should have an equal understanding of
the content material and concepts. When pairing students with differing levels, the roles of tutor
and tutee may be alternated, allowing the lower performing student to quiz the higher performing
student. Answers should be provided to the student who is lower achieving when acting as a tutor
in order to assist with any deficits in content knowledge. Same-age peer tutoring, like classwide
peer tutoring, can be completed within the students’ classroom or tutoring can be completed across
differing classes. Procedures are more flexible than traditional classwide peer tutoring
configurations.
How should tutors and tutees be selected?
One common method for determining dyads, or groups, involves ranking students from the highest
performing to the lowest performing student for the particular activity or subject. Pairs can be
formed by cutting the list in half and then matching the top performing student with the first lowest
performing student, the second highest performing student with the second lowest performing
student, and so forth . If heterogeneous groups are desired, the number of students in each team
should be determined. The list of students can then be numbered from one to the desired number of
persons in a group and then repeated until the entire class is included
When selecting tutors, teachers should be cognizant of which students can be most helpful in the
process. Teachers should be mindful of differing student personalities, needs, and preferences.
Dyads or groups should be established accordingly.
How should peer tutoring models be selected?
Peer tutoring models are flexible and can be altered to meet individual student or class learning
needs. The academic task should dictate the appropriate model based on content and learning
goals. While there is some upfront planning and instruction, once students develop an
understanding of procedures, groups or dyads can be altered dependent upon the setting, activity, or
desired learning outcomes.
How much instruction is needed to use peer tutoring?
Depending on the subject area and model selected, one to four, 30- to 45-minute sessions can be
devoted to teaching and modeling. Students should master each step of the model selected before

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learning additional skills. A teacher will need to closely monitor student progress to ensure that
established procedures are followed, students utilize interpersonal skills, and content is covered.
How should peer tutors be trained?
 Establish rules for confidentiality of student progress.
 Define and develop procedures for social skills students may need throughout peer tutoring (i.e.,
sharing, taking turns, using respectful language, and accepting criticism or feedback).
 Define and develop procedures for moving into peer tutoring groups quickly and quietly.
 Explain and model peer tutoring and allow students to practice prior to the first peer tutoring
session. Consider using a prepared script for practicing interactions (Fulk & King, 2001).
 Train students how to provide feedback for correct and incorrect peer responses, including praise.
 Teach students how to carefully monitor their own and their partner’s progress.
What can be done to support peer tutoring initiatives?
 Provide direct, systematic instruction for the peer tutoring process selected.
 Consider providing cue cards summarizing procedures or post procedures until automaticity is
established.
 Model error correction procedures.
 Chart, and consider posting, student or group progress.
 Praise use of tutoring procedures in addition to correct responses.
 Share with students the link between peer tutoring and increased achievement.
What is an ideal schedule for peer tutoring implementation?
Like the models and formation of groups, the development of a peer tutoring schedule is flexible.
However, it should be consistent. For example, peer tutoring can occur two to three times per week
for 20 minutes, with increasing student responsibility and fading of supports as students master the
selected peer tutoring process. However, it is important that student progress and procedures are
consistently monitored to ensure that accurate review and error correction occurs.
What steps are needed to plan for peer tutoring implementation?
Planning and Implementing a Peer Tutoring Program
 Clarify the specific objectives of the tutoring program, including both academic and social

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objectives when appropriate.
 List objectives in a form that can be easily measured.
For example: “Students serving as tutees will improve reading fluency by 30% on classroom
reading materials in the next 12 weeks.”
 “Performance of all students on weekly spelling tests will improve to an average of 85%; no
student will score lower than 60%.”
 “Within 8 weeks, students involved in tutoring will report that math is at least their third
favorite class.”
 Choose tutoring partners carefully. No firm conclusions can be drawn to direct tutoring
choices; nevertheless, several considerations should be taken into account. Some teachers
have recommended choosing students as tutors who are conscientious in class, and who
generally have to work for their grades. These teachers have believed that the brightest
students may have less empathy for students who do not learn easily, although, exceptions to
this are commonly found. Other considerations include the compatibility of the tutoring pair.
Teachers should find pairs who will work together well; however, they should also encourage
pairing students who are different in gender, race, or socioeconomic status whenever possible,
and not exclusively support established groupings.
 Establish rules and procedures for the tutoring program. These rules should cover how
students are to interact with each other, and specify the type of interactions that are not
acceptable. Procedures should specify the times and dates of tutoring, the materials to be
used, and the specific activities to be undertaken.
 Implement the tutoring program, monitor it carefully, and be consistent in enforcing the rules
and procedures. Modify rule and procedures as necessary.
 Evaluate the program frequently, and do not wait for the end of the program to determine
whether it was effective. Collect information throughout the program, and predict whether it
will be successful. If progress is not being made, modify the program.
What are some strategies for avoiding behavioral challenges?
 Use multiple sources of data to establish groups
 Provide cue cards.
 Post procedures.
 Review and model steps for providing constructive feedback.
 Reinforce students using specific, clear feedback.
 View challenges as teachable moments.

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 Evaluate and re-evaluate student pairings to determine success, and if necessary, rearrange pairs
accordingly.
HOW DO YOU KNOW IF TUTORING IS NEEDED FOR YOU
1. Geades are dropping.
2. Homework seems increasingly difficult.
3. Extreme anxiety before tests
4. Self estreem is dropping.
5. Loss of interes in learning.
6. Feelings of wanting to give up.
1. Provides personalized attention .
2. Improves grades.
3. Increases knowleage and
understanding of subjects.
4. Increasees motivation to succeed.
5. Provide intensive practice.
6. Allows progress at own pace .
7. Leads to bett use of study time.
8. Improves self- esteem and
confidance.
9. Encourages higher levels of
learning.
10. Provides praise , feedback and
encouragement.

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2nd meeting "Short-term exchanges of groups of pupils"
There is a saying that the best way to learn something is to teach it. At schools across the
world, students become better learners as they take the role of teachers and mentors to
younger children. Peer tutoring is also valuable because students can often forge stronger
bonds with other students than with adults and are more easily able to develop interest and
motivation in younger learners. While there are some problems with this approach including
the fact that not all students can be good teachers and also the quality of instruction may not
be as high as desired, still there are a lot of advantages to peer tutoring as set forth by
University of Western Australia below:
It involves students directly in the teaching and learning process;
 The act of teaching others enhances student's own learning;
 It encourages collaboration between learners;
 It can be viewed as a strategy for dealing with individual differences in the classroom.
Topic of Exchange: Peer Tutoring

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2. THE USE OF PEER TUTORING IN/WHEN STUDYING MATEMATHICS - Same-age
Peer Tutoring
The teacher
are teaching tutors
The tutors are
teaching tutees

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Tagram Designs
Tangram (Chinese: 七巧板; pinyin: qī qiǎo bǎn; literally
"seven boards of skill") is a dissection puzzle. It consists of seven
pieces, called tans, which fit together to form a shape of some sort.
The objective is to form a specific shape with seven pieces. The shape
has to contain all the pieces, which may not overlap.
History :
The Tangram very possibly originated from the yanjitu
(燕几圖) furniture set during the Song Dynasty. According to historical Chinese records, the furniture
set was originally a set of 6 rectangular tables. Later, an additional triangular table was added to the
set, and people can arrange the 7 tables into a big square table. There is some variation to such
furniture set during the Ming Dynasty, and later became a set of wooden blocks for playing. According
to other authors, the earliest reference to tangram appears in a
Chinese book dated 1813, which was probably written during
the reign of the Emperor Jiajing
Another legend states that a servant of a Chinese
emperor was carrying a ceramic tile, extremely expensive and
extremely fragile. The servant tripped, shattering the tile. In a
panic, the servant desperately tried to reassemble the tile into a
square, but could not. He spent many days trying to reassemble
the pieces into a square again, but could not, and instead
created thousands of patterns and pictures during his attempts.
While the tangram is often said to be ancient, its existence in the Western world has been
verified no earlier than 1800. Tangrams were brought to America by Chinese and American ships
during the first part of the nineteenth century.
The earliest example known is made of ivory in a silk box and was given to the son of an
American ship owner in 1802. The word "tangram" is built from TANG + GRAM. The word
"Tangram" was first used by Thomas Hill, later President of Harvard, in his book Geometrical Puzzle
for the Youth in 1848. The author and mathematician Lewis Carroll reputedly was a great enthusiast of
tangrams and possessed a Chinese book with tissue-thin leaves containing 323 tangram designs.

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Napoleon owned a Tangram set and Chinese problem and solution books while he was imprisoned on
the island of St. Helena. Photos are shown in "The Tangram Book" by Jerry Slocum. In 1903, Sam
Loyd wrote a spoof of tangram history, The Eighth Book Of Tan convincing many people that the
game was invented 4,000 years ago by a god named Tan. The book included 700 patterns some of
which are not possible.
While the tangram is often said to be ancient, its existence in the Western world has been
verified no earlier than 1800. Tangrams were brought to America by Chinese and American ships
during the first part of the nineteenth century. The earliest example known is made of ivory in a silk
box and was given to the son of an American ship owner in 1802. The word "tangram" is built from
TANG + GRAM. The word "Tangram" was first used by Thomas Hill, later President of Harvard, in
his book Geometrical Puzzle for the Youth in 1848. The author and mathematician Lewis Carroll
reputedly was a great enthusiast of tangrams and possessed a Chinese book with tissue-thin leaves
containing 323 tangram designs. Napoleon owned a Tangram set and Chinese problem and solution
books while he was imprisoned on the island of St. Helena. Photos are shown in "The Tangram Book"
by Jerry Slocum. In 1903, Sam Loyd wrote a spoof of tangram history, The Eighth Book Of Tan
convincing many people that the game was invented 4,000 years ago by a god named Tan. The book
included 700 patterns some of which are not possible.
Traditional tangrams were made from stone, bone, clay or other easy to get materials.
Nowadays they can be made from plastic, wood or other modern materials.
MATHEMATICAL PROOFS
Fu Tsiang Wang and Chuan-chin Hsiung proved in 1942 that there only existed 13 convex
patterns (i.e. patterns with no recesses in the
outline).
THE PIECES
Sizes are relative to the big abjh
square, which is defined as being of width,
height and area equal to .
 5 right isosceles triangles
o 2 small (hypotenuse1/2 of and sides
of 1/2 2)
o 1 medium size (hypotenuse of1/ 2)
and sides of1/2 )

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o 2 large size (hypotenuse of 1 and sides of 1/ 2))
 1 square (side of 1/2 2))
 1 parallelogram (sides of ½ and 1/2 2))
Of these 7 pieces, the parallelogram is unique in that its mirror image cannot be obtained by rotation.
Thus, it is the only piece that needs to be flipped when forming some silhouettes. Since there is only
one such piece, every possible silhouette or its mirror image can be formed with a set of one-sided
tangrams (for example, tangrams with a magnetic back that slide on a magnetic board).
LEARNING AND PLAYING TOGETHER
ACTIVITY SUMMARY
Buddypartners create designs using the traditional
seven pieces of a tangram. Usingone of their designs, they
make a tangram picture. !n preparation, the students learn
about the tangram and explore shapes and patterns by
arranging the pieces.
CONTENT AREAS: Maths, Arts
ACADEMIC AND SOCIAL FOCUSES:
• Identifying shapes
• Using shapes to create patterns
• Exploring spatial relationships
· • Sharing the work
• Reaching agreement
MATERIALS
BUDDY STUDENT PREPARATION
• Two transparencies of Tangram Puzzle sheet for each class
• Overhead projector
BUDDIES ACTIVITY
• Transparency of Tangram Puzzle sheet
• Overhead projector
• Tangram Puzzle sheets for each buddy pair
• Sheets of white or other light-colored
construction paper, scissors, and glue for each
buddy pair.

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BUDDY TEACHER PREPARATION
MODEL MAKING TANGRAM DESIGNS
There are many explanations and examples of tangram puzzles, pictures, and designs in
commercial products and books.
• Make two transparencies of the Tangram Puzzle. Cut out the tangram pieces on one
transparency for modeling making designs.
• Make photocopies of the Tangram Puzzle on paper in a variety of colors. Buddy partners will
choose from among the colored paper to make their designs
INTRODUCETHE TANGRAM ACTIVITY
• On an overhead projector, show
theTangram Puzzle transparency. Explain
that a tangram is an ancient Chinese puzzle
in which a square is
divided into seven shapes. The shapes can be
put together to make hundreds of designs.
Ask:
Q What shapes do you see in the tangram
image?
• As the students identify the shapes, point
them out on the transparency: five triangles,
one square, and one parallelogram.
• Explain that buddy partners will get a
Tangram ·Puzzle sheet like this. They'll decide
together· who cuts out the seven tangram
shapes. Then they'll make designs with the
shapes, decide which design they like best, and
glue that design onto a sheet of paper to make
a picture.
MODEL MAKING TANGRAM DESIGNS
• Explain that traditional tangram puzzles
require that you use all seven shapes, that
the pieces touch, and that no pieces overlap.
On the overhead projector, use the
transparency tangram pieces you made to
model making a few designs. Have a few
volunteers make designs with the
transparency pieces.
DISCUSS SHARING THE WORKAND
REACHING AGREEMENT
• Explain that during the session they will
need to share the work and reach agreement
with their younger buddy. Discuss:
Q How can you share the work of
making designs with your buddy?
Q How will you reach agreement about
what design to use in your picture?
INTRODUCE THE TANGRAM ACTIVITY
• On an overhead projector, show the Tangram
Puzzle transparency. Explain that a tangram is ·
an ancient Chinese puzzle in which a square is
divided into seven shapes. The shapes can be
put together to make hundreds of designs. Ask:
Q What shapes do you see in the tangram?
• As the students identify the shapes, point
them out on the transparency: five triangles,
one square, and one parallelogram.
• Explain that buddy partners will get a
Tangram Puzzle sheet like this. They'll decide
together who cuts out the seven tangram shapes.
Then they'll make designs with the shapes,
decide which design they like best, and glue
that design onto a sheet of paper to make a
picture.

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 Explain that traditional tangram puzzles require that you use all seven shapes, that the pieces
touch, and that no pieces overlap. On the overhead projector, use the transparency tangram pieces
you made to model making a few designs. Have a few volunteers make designs with the transparency
pieces.
DISCUSS REACHING AGREEMENT
 Explain that during the session they will need to reach agreement with their older
buddy.
Discuss:
Q How will you reach agreement about what design to use in your picture?
Q If you and your buddy disagree, what can you do to try to reach agreement?
GET READY TO WORK TOGETHER
• Have buddy partners find a comfortable place to work.
• On the overhead projector, show the tangram transparency. Explain that:
• Each pair will get a copy of the Tangram Puzzlein a color they choose.
• Partners will decide who cuts out the seven tangram shapes.
• Togethe rpartners will use the shapes to make designs.
• Partners will agree on a design to use in their tangram picture.
• Partners will glue the design to a piece of construction paper to maid!a picture.
• Partners will write their names on their picture.
TIP You may want to write the steps of the activity on the board.
DESIGN TANGRAMS
• Have pairs select the color Tangram Puzzle they want. Distribute the construction paper,
scissors, and glue. Have them begin their project.
CIRCULATE AS BUDDIES WORK
• If necessary, support buddy partners as they work by asking:
Q What other designs can you make with the tangram shapes?
Q What can you do if you don't agree on a design for your picture?
Q How can you share the work of [gluing the pieces to the construction paper]?
• If partners finish early, have them make another picture.
SHARE POSTERS AND REFLECT AS A GROUP

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• Gather all buddies. Have a few volunteers share their pictures with the group.
• Briefly discuss:
Q What are some ways you helped your buddy today? What are some ways your buddy helped
you?
• Collect the pictures for display.
DISCUSS THE BUDDIES ACTIVITY
• Back in their classroom, have the students reflect on how they worked with their younger
buddy:
Q How did the activity go today? Do you think it was successful? Why?
Q If you and your buddy didn't agree about a design for your picture, how did you reach
agreement? How did this work for you?
DISCUSS THE BUDDIES ACTIVITY
• Back in their classroom, have the students reflect on how they worked with their older buddy:
Q If you and your buddy didn't agree about a design for your picture, how did you reach
agreement? How.did this work for you?
Grandfather Tang’s Story by Ann Tompert

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School Day of Non-violence
and Peace- on January