Long Ago and Even in Ourpresent Times There Are Teachers Who Still Use the Chalk and Talk

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Long ago and even in ourpresent times there are teachers who still use the chalk and talk method and are very student centered. But because we are dealing with students of different levels of abilities and understandings, not all the students learn Geometry via this method?

With theaidof the appropriate and consistent resources in Geometry in the mathematics curriculum, enable teachers to use a more student-centred approach based on the constructivist Piaget's theory of constructivism impacts learning curriculum because teachers have to make a curriculum plan which enhances their students' logical and conceptual growth. Teacher must put emphasis on the significant role that experiences-or connections with the adjoining atmosphere-play in student education. For example, teachers must bear in mind the role those fundamental concepts, such as the permanence of objects, plays when it comes to establishing cognitive structures. And therefore with the help of resources in geometry, no child is left behind.http://www.teach-nology.com/currenttrends/constructivism/piaget/

Resources issomething that one uses to achieve an objective.And Geometry helps us to represent and describe in an orderly fashion our geometric world. The learning of geometry was done by the Dutch psychologists Pierre van Heiles and Dina van Heile-Geldof. They suggested that with appropriate instructional opportunities, children move through a succession of stages of increasing abstraction relative to their thought development in geometry.http://nrich.maths.org/2487

Resources may include

1.•Tangrams

Developing Geometry Understandings and Spatial Skills through Puzzlelike Problems with Tangrams: Tangram Puzzles

Describing figures and visualizing what they look like when they are transformed through rotations or flips or are put together or taken apart in different ways are important aspects of geometry in the lower grades. This two-part tangram example demonstrates the potential for high-quality experiences provided by computer "shape" environments for students as they learn concepts described in theGeometry Standard.Problem-solvingtasks that involve physical manipulatives as well as virtual manipulatives afford many students an entry into mathematics that they might not otherwise experience. In this part, Tangram Puzzles, students can choose a picture and use all seven pieces to fill in the outline. In the second part, Tangram Challenges, students can use tangram pieces to form given polygons.

Getting Started

Young students' experiences with puzzles provide a background for undertaking this activity. Because similar puzzles are available for use with plastic or paper tangrams, students can move back and forth between concrete materials and the computer environment. After the students have had time to work with the outlines, teachers might ask them questions such as the following, which challenge them to try different solutions or to reflect on the strategies they used to solve the puzzles:

·  Can you fill the outlines in another way?

·  How many different ways are there to fill in this shape?

·  What do you do when you cannot figure out a puzzle?

·  Can some tangram pieces substitute for others?

What Students Learn

Whereas completing the same or similar puzzles with both physical and computer manipulatives may help students generalize their experiences, the computer environment is likely to encourage them to think about how they need to manipulate the tangram pieces rather than approach the task mainly by trial and error. Working with a partner at the computer to complete puzzles also encourages students to become more precise in their use of vocabulary about space. Teachers can enrich students' vocabulary in class discussions by these comments on students' actions, such as "I see you are rotating the parallelogram " or "What difference would flipping make?"

http://www.lessonplanet.com/search?keywords=geometry+shapes+tangram&media=lesson-

Students explore properties and relationships of geometric shapes through the use of tangrams. They create an example of symmetry using tangram pieces and list properties and give examples of similar and congruent polygons.

Students study polygons and tangrams. They experiment with various polygons and create their own tangrams. They create a PowerPoint presentation to illustrate and explain polygons, symmetry, area and perimeter.

Students investigate and predict the result of putting together and taking apart two-dimensional shapes. They are told that they are going to receive a set of tangram pieces. Students are explained that tangram pieces can be used to make new shapes by matching the edges of two or more pieces. They are divided into groups of three or four students, they work in groups together to find the tangram pieces that fit exactly into the shapes on the BLM Tangram Shapes.

Students investigate the concept of creating different shapes using tangram pieces. They determine a number of combinations that can be used to create different shapes. Each student creates their own set of tangram shapes by cutting them out of paper.

Students construct the tangram pieces from a square paper by following directions to fold and cut.

Students explore geometry related to real-world situations and tangrams. They explore a math website, identify various shapes, draw and describe shapes, read about the history of tangrams, and create their own set of tangrams out of paper.

Students use tangrams, student literature, and Websites to explore shapes.

Describing figures and visualizing what they look like when they are transformed through rotations or flips or are put together or taken apart in different ways are important aspects of geometry in the lower grades. This two-part tangram example demonstrates the potential for high-quality experiences provided by computer "shape" environments for students as they learn concepts described in the Geometry Standard.

Students explore how shapes have parts and those parts have relationships which leads to dissection and reassembly and ultimately to the concept of congruence. They identify, describe and compare congruent 2-dimensional geometric figures by cutting out a tangram puzzle.

Students explore surroundings to find geometric shapes, and practice creating polygons on Microsoft Word drawing toolbar. Students design quilt squares to be attached to class quilt.

PENTOMINOES

ORIGIN

Pentominoes are thought to have been “invented” by Solomon W. Golomb in 1953, during a talk he gave to the Harvard Mathematics Club.He is credited with coining the name pentominoes, but they have been around since a much earlier time.Henry Ernest Dudeney, a great English inventor of puzzles, created the first pentomino problem, which was published in the Canterbury Puzzles in 1907.

CHARACTERISTICS

Apentominois ageometric shapecomposed of five (Greekπέντε/pente) identical squares, connected orthogonally. Compare this to adomino(two squares),tetromino(four squares), orpolyomino(any number of squares).

There are twelve different pentominoes, and they are named after letters of the alphabet.

Themirror imageof a pentomino does not count as a different pentomino. For example, the eight possible orientations of the Y pentomino are as follows:

ADVANTAGES OF USING PENTOMINOES

•Provide intriguing puzzles, interesting patterns, and exciting games

•Nurture a non-anxious and positive attitude toward math and science

•Promote an atmosphere of cooperation

•Develop the problem solving process

•Supply spatial-ability skill exercises

•Serve as concrete representations to understand abstract ideas

SOME APPLICATIONS IN MATHEMATICS

(Big Ideas/Concepts)

Congruence, flips (reflections), slides (translations), turns (rotations), area and perimeter, tessellations

RECOMMENDED ACTIVITIES

i)Making Pentominoes

Students try to build as many distinct pentominoes as possible using square blocks, or construct them using graph paper.

ii)Area and Perimeter withPentominoes/Graph Paper

Students engage in an enrichment lesson usingpentominoes,exploring the concepts of area and perimeter. They construct new distinctpentominoesusing graph paper and then identify the area and perimeter measurements of each. They discover how shapes with the same area can have different perimeters.

iii)Pentomino Puzzles (Rectangles)

Use all 12 pentomino shapes to create rectanglesof varying dimensionsA standard pentomino puzzle is to arrange a set of the twelve possible shapes into a rectangles without holes, e.g.3x20, 4x15, 5x12, 6x10.

iv)Interactive Pentominoes games online

Play pentominoes online athttp://www.gamepuzzles.com/polyintr.htm#Background

v)Play the Game!

Make ‘checkerboards’ of 8x8 one inch squared paper.Take turns placing pieces on the board with the winner being the last person to place a piece.Try other rectangular boards such as 5x12.Variations include using just one set of pentominoes between two players, or each player using one set (allows for a shape to be used twice).Another variation is to make the last person to place a piece be the loser!

vi)Pentominoes and Net of a Cube

a)Given the 12 distinct pentominoes,students are asked “which pentominoes do you think will make a box (open cube)?” They make predictions and then cut out the shapes and try to form a box.

b)Have children save (and wash!) milk cartons.Cut off the top to make an open box.Students then cut the boxes into the different pentominoes.

c)Have students visualize folding the sides to make an open box.Then fold pentominoes to check their guesses.Mark an X on the square that is the bottom of each box.

vii)Pentominoes and Algebra Graphing,: Using 12 Shapes to Help Students Graph

Using a transparency grid (half-inch or one centimeter grids work well) and pentominoes cut to the same size grid make a great visual aid that can be used over and over for demo purposes. Starting with the simplest shape, the I, coordinates of the four vertex points are easily recorded. Students then explore the results of specified transformations of the shape (reflection, translation and rotation). Questions may be asked to build students’visualization and prediction skills(e.g. How would the coordinates of the vertices change if the ‘I’ shape was reflected in the y-axis?). The degree of difficulty is gradually increased with the less simple pentominoes.

http://www.lessonplanet.com/search?keywords=geo+boards&media=lesson

GEOBOARDS

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the English mathematician and pedagogist Caleb Gattegno (1911-1988) as a manipulative tool for teaching elementary geometry in schools. The applications range from the comparison of shapes to the arithmetic computation of areas (e.g., Pick's theorem), and the study of transformations in the plane

Students explore geometric shapes. In this geometry lesson, students readThe Greedy Triangleand examine polygons. Students usegeo boardsto create polygons and use polygons to build a "peculiar person".

Students read poetry and build their vocabulary through use of the puppet Geo George.

Students explore the differences between right, acute, and obtuse triangles. In this geometry lesson, students will research Internet for information on angles and triangles. Students will practice making the different types of triangles usingGeo boards.

Students use shape puppets to review geometry content. They take turns singing songs, reading students poems, reciting class bulletin board notes and choral poems. They prepare for their summative assessments through play and interview questions.

Students create pictures using a geoboard and straws using the X and Y axis.

Students review geometry unit content through a vocabulary/word game. They demonstrate understanding using geoboards to answer questions. They work in groups and it's a race to the correct answer.

Students learn five songs to define and develop understanding of the attributes of two- and three-dimensional figures and the meaning of mathematical terms. They classify objects as either two- or three-dimensional, through the use of the songs.

Students, in groups, use song lyrics and math to descrie two and three dimensional shapes.

Students explore geometric vocabulary through creation of shapes on a geoboard. They present design attributes, transfer of design, and color-coding components mix to create a fun and exciting lesson that stretches student thinking.

Students experiment with, identify, and follow teacher-directed instruction toward understanding two-dimensional geometric shapes found within the environment. Groups of students utilize geoboards to help them explain geometric shapes.

Computer and

Software-

Math Manipulativeshttp://www.ct4me.net/math_manipulatives.htm-

Math Manipulatives contains resources that enable students to interact online

About Virtual Manipulatives

What is a virtual manipulative?

InWhat are Virtual Manipulatives?, Patricia Moyer, Johnna Bolyard, and Mark Spikell (2002) defined a virtual manipulative as "an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (p. 373). Static and dynamic virtual models can be found on the Web, but static models are not true virtual manipulatives. Static models look like physical concrete manipulatives that have traditionally been used in classrooms, but they are essentially pictures and learners cannot actually manipulate them. "...[U]ser engagement distinguishes virtual manipulative sites from those sites where the act of pointing and clicking results in the computer's providing an answer in visual or symbolic form" (p. 373). The key is for students to be able to construct meaning on their own by using the mouse to control physical actions of objects by sliding, flipping, turning, and rotating them.