Thursday, February 26, 2009

Social Constructivism

Social Constructivism

I can use cognitive apprenticeship in my 2-D geometry lesson plan. I will be the expert and guide my students toward gaining knowledge about the different geometry symbols. Students will first observe me using my body to demonstrate the different geometry symbols. We will then do it together and I will coach, provide feedback, and give reminders about the different symbols we are demonstrating through our body movements. I will use scaffolding while teaching by gradually modeling less and having students create the movements on their own. I then give them more responsibility in the Geometry says activity, and lastly I have them go search for the symbols around the room on their own. I will ask questions throughout the activity where students have to address what they are doing because of what they learned. Have students talk about what they have been learning and how their movements have improved throughout the lesson. Ill ask what movements we did together and where they took them from there. They then have to explore new ways to apply what they are learning. They have to create movements on their own. They then get to play Geometry says, where they have to be creative and come up with movements on their own. They then have to go around the room and find examples of the shapes, angles, and lines that they had been creating movements for. This will make them think deeper and make other connections. Some tools I will use is putting pictures of the symbols up on the board, for the students to see. When they use their bodies to create the symbol that is also a tool. I will make sure to know each and every one of my students so that when I am teaching I will be know how to reach all of their zones of proximal development. I will have prepared them with the material needed before this activity beforehand. After teaching the lesson I will refer back to this lesson many times, so the material learned will be maintained.

Tuesday, February 24, 2009

Virtual Tour

Location ActivityGoogle Earth Content
1. Battle at Lexington and ConcordRead the poem "Paul Revere's Ride" by Henry Wadsworth Longfellow and then have students create a poem of their own about Paul Revere or the BattleArlington,MA (Middlesex county)
2. Battle of TiconderogaDo a play where they take over the fort with no shots fired
Ticonderoga, New York
3. Battle of SaratogaHave students create a diorama or poster depicting their favorite part of the Battle at Saratoga
Saratoga, New York
4.Battle at Valley ForgeDebate between George Washington and his troops. Washington wanted to keep fighting and the troops wanted to head home
Cache-Control: max-age

Virtual Tour Challenge

Social Studies, Fifth Grade, Standard 2, Objective 2a. Plot a time line of the key events of the Revolutionary War

Thursday, February 19, 2009

Developmetnal Cognitivism

Developmental Cognitivism

Stage Based Learning

According to Piaget the students I am teaching (third grade) this lesson to are in the concrete-operational stage. This stage encourages a lot of “hands on” thinking. Students can realize that elements can be changed or transformed and still conserve many of their original characteristics. My lesson incorporates a variety of different ways to symbolize the geometry terms. For example, I have them show the symbols with their bodies, I then have them play Geometry says, and then have them look for the symbols around the room. The children are able to realize that even though each symbol is a different, size, shape, color, or medium that it still represents the same thing. This lesson is all hands on, it is the students and I working with lines, shapes, and angles in a variety of different interactive ways.

Uniqueness of Individual Learning:

This lesson allows for a lot of children variability and creativity. When representing the symbols by using their bodies they have the freedom to go as far as their mind will take them, or as simple as is comprehendible for them. When they walk around the room to observe the different symbols they can observe the most basic aspects or the most abstract aspects. By providing a variety of activities to teach about the geometry terms it is more likely that all of the students needs will be met in one way or another.

Experience that Involves Action

The entire lesson is full of action. They get up and move around to experience shapes, lines, and angles through the use of their body. This will help them to make connections with the terms and how they use their bodies to represent them. They get to play Geometry says where they move around have freedom. They then get to walk around the room and observe the geometry symbols all around them. By having these action activities students are able to make connections with their actions and the terms.

Necessity of Social Interaction

Throughout the lesson the students will have the chance to interact with one another. When they use their body to show the symbols they will all be in the same vicinity, where they can feed of each other’s ideas and energy. It will be great for them to even work together to create the symbols. When playing Geometry says it will be similar to the environment of the body activity. They will get to help and inspire creativity in one another. When making observations around the room they can work with each other and give each other ideas as well. Social interaction is crucial for student learning at their young age.


In the 2-D geometry lesson assimilation and accommodation can be utilized by students to help learn the material. They use assimilation by connecting the new information into old schemes. An example of this is if any of the students have ever danced before they can make a connection between the movements they use in dance and the geometry terms. Another example would be to take what they know about different objects in the room and connect the geometry term to it. For example, they look at the white board and see 4 right angles. They are connectin g new information with schemes they already have. When students accommodate they create new schemes or adjust old ones in response to new information. An example of this is when they play Geometry says. Their prior knowledge of Simon Says is adjusted to be Geometry says. The rules then change in their minds because they have to show shapes, lines, and angles.

Disequilibrium/cognitive dissonance

At first when students are asked to use their body to show examples of terms that they barely know they will experience disequilibrium. The students will realize they do not fully understand so they will use assimilation and accommodation to learn the material. It is during this disequilibrium that students will learn the most.


Throughout the lesson I will try and appeal to the student’s different schemas. I will help them create schemas by having them do different behaviors (actions). When they do the motions with their bodies, bplay geometry says, and record different objects around the room they will use different behaviors to create a schema. I also will appeal to their symbolic schemas by showing the symbols for everything on the board, having them use their bodies to show the symbols, and making connections to things around the room.

Discovery learning

Students will learn through their own discoveries. I will not tell them exactly what body part to use to make the shapes. They will have the chance to be creative and discover all the different ways to use their bodies to make the symbols. They also will go around the room and discover for themselves these objects.


I will group the terms into different categories so that the students will be able to classify the different groups and symbols within. For example we will first go over different lines. Then we will go over different angles. Lastly, we will go over different shapes. Students will be able to make these classifications. The more advanced they get on the terms they will then be able to make the connection that some of the classes fit into each other.

Thursday, February 12, 2009


2-D Geometry: Behaviorism

The purpose of this lesson is for students to be able to demonstrate their understanding of Geometry by naming and identifying different lines, shapes, and angles through the use of their bodies and critical thinking.

Learning Task:
1. Show students different ways to use your body to show shapes,lines,and angles.
2. Have the students model what you are doing
3. Have students create the shapes,lines,and angles on their own
4. Play Geometry says with the students where they use their body to show the shapes,angles, and lines
5. Have students search for real objects in the room that are angles,lines, and shapes

Positive reinforcement

I will use positive reinforcement throughout the lesson to increase student’s behavior. When they are doing the right motions I will comment on them being correct. When students stay standing in Geometry says I will give them a reward.
When students are quietly making observations around the room I will make comments about what they are doing right. When students are giving good descriptions to one another they will get rewards for doing it correctly.

Reinforcement Schedules

By having the students play Geometry says I will use variable fixed-ratio. I will state the term and students have to demonstrate using their bodies the term. If students get it wrong they have to sit down. Students that continually stand up until the end get a reward. Students will realize that the number of times I say Geometry says will not be constant. I will try and make it unpredictable so students will try and stay in the game as long as possible, by doing the right symbols.

Premack Principle

By having the students do the movement activity, geometry says, observing the classroom, and descriptions for each other they are doing preferred activities. When I say preferred I mean that they are more fun for a child to do than worksheets and countless problems from the book. However, for homework they may need to do worksheets, so by doing these more preferred activities to begin with they serve as a reinforcer for the less preferred activities (worksheets, book work, etc.)

Vicarious Reinforcement

One way to help students learn the terms is to have them use their bodies to show what a shape, angle, or line looks like. When students are demonstrating the geometry symbols correctly then I will give them positive reinforcement. I will point out specific students and say why what they are doing is right. By doing this hopefully the students that are doing it incorrectly will observe what is correct.

Observational Learning

I will increase students learning by helping them observe myself and others. I will keep their attention throughout the activity by staying excited and keeping the pace up. So during the body movement activity I will model this behavior in hopes that they will model my behavior. By engaging all of their different senses it will help them retain the material better. I will use visuals, kinesthetic, and audio cues to help them retain the geometry terms. I will then have them practice what they learned through all of the different activities so they can master the terms. I will try and keep the students motivated by not staying on any one activity for too long and keeping the material upbeat. I will reinforce the students when they are doing things correctly so they will continually do it correctly.

Tuesday, February 10, 2009

Monday, February 9, 2009

2-D Geometry

Through the use of several different cognitive learning principles my lesson plan will stick in my students’ long-term memory.

Attention and Sensory Memory

One of the key aspects to an effective lesson is a hook. The main reason a hook should be used is to grab the student’s attention. Hooks get the students excited and prepared for what they are about to learn. Our sensory memory is the initial processing that transforms incoming stimuli into information so it will make sense to us. Having attention and perception are extremely important at this stage, that is why hooks are so crucial in a lesson plan. For the 2-D Geometry lesson plan the hook is demonstrating the geometry vocabulary words through body movements. I will create different body positions and movements and the students will mirror me. An example would be to use your arms to show what a right angle would look like. Then I would have them think of different ways to use their bodies to show a right angle. An activity like this keeps the students attention while they are processing the information.

Working Memory

Working memory has very little capacity. There are several strategies that can be used to turn working memory into more concrete. First off working memory needs to be kept activated to be retained. This concept is reinforced throughout the entire lesson plan. The lesson first focuses on ten angles or forms of lines when we do the movement activity. We then play Geometry says using the lines and angles vocabulary. Then the students explore different lines and angles around the room. The geometry vocabulary keeps getting activated throughout the lesson. Some strategies of retaining information in working memory are elaborative rehearsal and chunking. A way that elaborative rehearsal is used in the lesson plan is by having them go around the room and find the angles and shapes. This helps them make connections to things they already know. Another activity that encourages elaborative rehearsal is the Geometry movement activity because they are associating movements of their body with the angles or lines they make. Students are also able to use chunking to process the information they are learning. The first part of the lesson focuses on lines and angles. Then the second part of the lesson focuses on shapes. By chunking lines, angles, and shapes into their own categories it is easier for children to retain the vocabulary terms.

Long-Term Memory, Declarative Knowledge, and Procedural Knowledge

The two types of knowledge, declarative and procedural, are taught throughout this lesson plan. Declarative knowledge is taught by simply making the connection between the shapes, angles, lines and connecting them with the symbols that represent those terms. These geometry terms are simply declared through words and symbols. Procedural knowledge is taught about these geometry concepts because they are taught how to create these geometric patterns and symbols. They also use procedural knowledge when they correctly categorize the shapes, lines, and angles. By using all these different activities students are able to store information about these geometry terms and symbols both visually and verbally. One way to store things long-term is through elaboration, which we discussed previously. Another way that things are stored long-term is through organization. The way this lesson is arranged all of the concepts are very organized, which will help the students to store it in an organized fashion.


Through the use of several mnemonics strategies the concept being taught will more likely stay in the student’s memory. One way to help the students remember the shapes, angles, and lines is by using the Loci method. The loci method is when you associate items with specific places. This is used in the lesson when I have the students go around the room to find the shapes, angles, and lines with objects in the classroom. These locations will also serve as “pegs.” By having the students categorize the terms with the locations they are using peg-type mnemonics. Another way that I could help my students remember the geometry terms is to create an acronym. An acronym I could use for the shapes would be “The Queen Painted Her Hen Orange” (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon). Distributed practice is also a great way for children to retain memory. Distributed practice is when you practice in brief periods with rest intervals. I would reinforce these concepts over several days, so that the students have time to register the material, have a break, and then practice some more.

Wednesday, February 4, 2009

Psychology Lesson Plan

2-D Geometry

Curriculum Tie:

* Visual Arts
3rd Grade
Standard 1
Objective 1
* Language Arts
3rd Grade
Standard 1
Objective 1

A variety of activities to help students understand geometric terms, angles and shapes.

Main Curriculum Tie:
Mathematics - 3rd Grade
Standard 3 Objective 1
Describe and compare attributes of two-dimensional shapes.


* Math Journal
* 3” x 5” cards
* pencils
* colored pencils
* 12” ruler
* scissors
* Power polygons
* Geometry Concentration Cards
* Name That Angle
* Classify Shapes

Additional Resources


* Twizzlers, by Jerry Polatta ISBN: 0613678605
* Three Pigs, One Wolf and Seven Magic Shapes by Grace Maccarone & Marilyn Burns ISBN: 0590308572


* geometry_concentration_cards.pdf
* classify_shapes.pdf
* name_the_angle.pdf

Web Sites

* Illuminations

Background For Teachers:

Geometry is more than just naming lines and shapes. Geometry also includes moving, combining, and comparing lines and shapes. Students need to explore kinesthetically in order to better understand different geometric ideas and concepts.


* Line – a straight path continuing without end in both directions.
* Point – an exact location in space represented by a dot.
* Line segment – a part of a line with two endpoints.
* Ray – a part of a line that has one endpoint and goes on forever in one direction.
* Horizontal line – a line that is parallel to the horizon. A horizontal line is straight across.
* Vertical lines – a line that has right angles to the horizon. A vertical line is straight up and down.
* Intersecting lines – lines that meet or cross at one point.
* Parallel lines - lines in the same plane that are always the same distance apart - that do not cross.
* Angle – formed by two rays or two line segments with a common end point.
* Right angle – an angle that forms a square corner—measures exactly 90 degrees.
* Obtuse angle – an angle with a measure greater than 90o and less than 180 degrees.
* Acute angle – an angle with a measure less than 90o.
* Polygon – a closed plane figure made by three or more line segments.
* Quadrilateral- a four-sided polygon with four sides.
* Pentagon – a polygon with five equal sides
* Hexagon – a polygon with six equal sides
* Octagon – a polygon with eight equal sides
* Parallelogram – a quadrilateral with two pairs of parallel and congruent sides.
* Similar – same shape – not necessarily the same size
* Congruent – having exactly the same size and shape.

Intended Learning Outcomes:
3. Reason mathematically
4. Communicate mathematically
5. Make mathematical connections

Instructional Procedures:
Invitation to Learn

Invite students to come to the floor. Demonstrate to the students each vocabulary word with your body and have students mirror the body positions associated with each geometric term.

* Line – a straight path that is endless in both directions (a line must be straight).
* Point – an exact position on a line.
* Line segment – part of a line with two endpoints—line segments have a beginning point and an end point.
* Ray – part of a line that is endless in one direction—has a starting point but no end point.
* Horizontal lines – lines that go left and right. (across the horizon)
* Vertical lines – lines that go up and down.
* Intersecting lines – lines that cross at one point.
* Parallel lines - lines that do not cross. (lines are same distance apart)
* Angle – formed by two rays or two line segments with a common end point.
* Right angle – an angle that forms a square corner—measures exactly 90 degrees.

Show students what a “right angle” looks like with both arms (in several different ways—going out to the right and other hand down— top right, top left, bottom right, bottom left.

* Obtuse angle – an angle with a measure greater than 90 degrees and less than 180 degrees—greater than a right angle.
* Acute angle – an angle with a measure less than 90 degrees— smaller than a right angle.

Have the students stand and play Geometry Says (Simon Says): with the geometric terms. When a student gets one wrong, they sit down. The last student standing is the winner. You may want to do this in pairs or triads to give students with the most need for repeated practice partners to work through the experience.

An optional way to assess students’ knowledge is to place students into small groups and give a point to the first group that has all the students with the correct position. Or the students as a team have to show the geometric term (standing, connecting arms).

Instructional Procedures

1. After playing Geometry Says, have students draw a picture and label each of the geometric terms learned in their math journals. Have the students explain to each other in small groups (think, pair, share) the similarities and differences between the different lines and angles.
2. Give students each a 3”x 5” card. Students will use it to explore right, acute, and obtuse angles in the classroom. Have students discuss their findings with the class.
3. Next, have students describe to their neighbor the difference between square and a triangle. They need to be able to describe these shapes using geometric vocabulary.
4. Teacher demonstrates drawing a shape and describes it with types of lines and angles. For example: Draw a vertical line segment about one inch long. Next, draw a horizontal line segment that is about one half inch long (half the length of the vertical one) starting at the bottom of the vertical line segment and going to the right making a right angle. Last, draw a line segment that connects the top of the vertical line and the far right of the horizontal line creating two acute angles.
5. Divide the students into pairs. Have each student draw a shape in their math journals using line segments. Then without showing that shape to their partner, describe the shape (using names of lines and angles) they have drawn to see if their partner can produce a shape that is similar.
6. Explain to students the difference between similar and congruent shapes. Using power polygons have students find similar and congruent shapes.
7. Pass out a power polygon and have students draw and describe it in their math journals. After discussing it with the class, have the students label it with the geometrical shape name.

* Polygon – a closed figure with three or more sides made up of line segments.
* Quadrilateral- a polygon that has four sides.
* Pentagon – a polygon with a five equal sides.
* Hexagon – a polygon with six equal sides.
* Octagon – a polygon with eight equal sides.
* Parallelogram – a quadrilateral with exactly two pairs of parallel and thereby also having two pairs of congruent sides.

* angles.gif
* angle.gif

Curriculum Extensions/Adaptations/ Integration

Line segment star art: You will need white art paper, pencil, ruler, colored pencils, scissors, and contrasting colored paper to mount finished design.

* Place two dots three to five inches apart in the center of the paper. Lightly label the endpoints one and two.
* Connect the two dots with a ruler to create a horizontal line segment.
* Draw about ten dots all over the paper (avoid the horizontal line segment itself and the area if the line segment were extended to the edge of the paper)
* Use a ruler to draw a straight line starting at endpoint one, out to a scattered point, and then from the scattered point to endpoint two.
* Continue the pattern with other scattered dots around the page.
* Design and color each individual section created by intersecting line segments with colored pencils.
* Outline star with black, cut out and place on contrasting colored paper.
* Have students point out an acute angle, obtuse angle, and see if they have any right angles in their design.
* Extend the learning for students with special needs by using students’ bodies to demonstrate lines and angles in Geometry Says.
* This lesson integrates writing and art with geometry.

Family Connections

* Have students use the 3” x 5” card to find angles at home. Students can write the type of angles they found and bring them back to share with the class the next day.

Assessment Plan:

* Using students’ math journals teachers can assess what students learned.
* Students can demonstrate knowledge of correct geometrical terms by matching pictures to definitions described using Geometry Concentration game.
* Students can draw and create a picture labeling lines, shapes, and angles.
* Watching students play Geometry Says to see if they can show different lines and angles.
* Other resources: Name that Angle
* Classify Shapes—one sheet per student.

Research Basis

Clements, D. H., & McMillen, S. (1996). Rethinking concrete manipulatives [Electronic Verson]. Teaching Children Mathematics, 2(5), 270-279. Retrieved July 5, 2004, from Ebscohost database.

This article discusses what mathematical manipulatives are and how they might be used effectively. It also gives definitions of types of manipulatives and how to select and use them effectively.

Pickreign, J. (2000). Alignment of elementary geometry curriculum with current standards [Electronic version]. School Science & Mathematics, 100(1), 243-251. Retreived April 24, 2004, from Ebscohost database.

The subject of geometry in the curriculum is an area of concern among educators. This article identifies models for acquisition of geometry with concrete modeling, pictorial modeling, real-world situation, oral language, and symbolic representations.

Utah LessonPlans

Created Date :
Jun 27 2006 08:29 AM

Digital Story TPACK

What is the content you’ll be using in your lesson?

The content that I will teach for my lesson is developing language through viewing media and presenting (Language Arts Standard 1). My students will also write in different forms and genres (Language Arts Standard 8).

What is the pedagogy you’ll be using and why is it a good fit with the content?

My student's will create a poetry interpretation using media devices. My students will choose a poem (the poem I chose was Shel Silverstein's A Bear in There). They will then present that poem through a media device. They will be required to have the writing, pictures, music, and their voice reading the poem. This pedagogy fits great with the content I am teaching. The students are developing their language through reading the poems, writing the poems, and thinking about what the poems mean (they will show the meaning through the pictures they choose or create). They also can choose poems from all different genres, which will help them when it comes time for them to write poems in different genres.

What is the technology you’ll be using and why is it a good fit with the content and pedagogy?

The technology I am going to use is Photostory. This is such a great resource to use in the classroom! It is great for children of all ages. Photostory is the perfect tool to effectively teach the content and use the designated pedagogy. It is great because it allows the students to create their presentations. They can add music, writing, vocal recordings, and pictures. Since I can use this form of pedagogy it enables me to teach the content I specified. The children will be able to develop language through viewing and presenting media. They will also be able to write in different forms and genres. The technology, pedagogy, and content, fit together perfectly.

Tuesday, February 3, 2009


Bear in There
By Shel Silverstein

Monday, February 2, 2009

Phases of Moon TPCK

What is the content you are focusing on in your science lesson?

The content that we focused on was the phases of the moon. More specifically, we studied how the appearance of the moon changes over a 31 day period of time. This is taught to students in the sixth grade. It is very interesting and fun to learn about.

What is the pedagogy you are using and why is it a good fit with the content?

The pedagogy being used is predicting, observing, and acquiring data. These concepts are great pedagogy tools to be used with teaching the phases of the moon. First, the students predict how they think the phases of the moon will change throughout the month. This gets the students really thinking hard about the phases of the moon. Then they observe how the moon changes throughout the month. They can cross check their predictions with their observations to see if they are correct. Lastly, the students will compile all of their data from their observations and predictions. it is a great way to incorporate your content with pedagogy strategies.

What is the technology you’ll be using and why is it a good fit with the content and pedagogy?

The technology used was Stellarium. This is a really neat internet site that allows you to observe all sorts of things in space. It is the perfect tool to use that can implement the content and pedagogy ideas already mentioned. Since the content we are teaching is the phases of the moon I used Stellarium to show how the moon changes throughout the month. It is so convenient and quick. It is really helpful so the students don't have to go outside every night to observe. It is available to them right at their fingertips. It is a great fit with the pedagogy because it allows students to predict, observe, and acquire data. The content, pedagogy, and technology combined create a powerful lesson.