# data[].attributes.body
·         Lev Vygotsky studied children and how they learned.

·         He theorized that learning is a social interaction within their culture.

·         Social interaction learning takes place in two ways:

o   First, on a social level between people  - interpsychological

o   Second, inside the child – intrapsychological

# data[].attributes.body
·         An additional aspect of Vygotsky’s social theory is the Zone of Proximal Development (ZPD)

·         There are three parts to ZPD:

o   What I can’t do

o   What I can do with help

o   What I can do

# data[].attributes.body
• Children must have social interaction to progress in cognitive development.
• Cognitive development in isolation is limited; however, social interaction within their culture allows children to reach full cognitive growth.

# data[].attributes.body
o A child does not inherently know numbers.
o A child can start to learn numbers during social interaction with a parent/teacher/peer.
o A child knows numbers on their own.

# data[].attributes.body
Constructivist theory states that people make their knowledge through experience, prior knowledge, and new events, according to Jerome Bruner.

# data[].attributes.headline
There are two main principles of the constructivist theory:

# data[].attributes.subject
There are two main principles of the constructivist theory:

# data[].attributes.body
o   First, learning is not innate; it is constructed through the foundation of prior learning.

§  The previously learned information will influence what an individual does with the new information being learned.

o   Second, learning is not passive; it is an active process.

§  Teachers must actively involve students in real-world problem solving or experiments to construct meaning.

§  Students must make meaningful connections during the learning process between the prior knowledge and the new information.

# data[].attributes.headline
All learning and teaching is socially constituted knowledge based on sharing and negotiating

# data[].attributes.subject
All learning and teaching is socially constituted knowledge based on sharing and negotiating

# data[].attributes.body
o   The works of Lev Vygotsky (sociocultural theory) and Jean Piaget (cognitive theory) are two integral theories for constructive learning.

# data[].attributes.headline
Many activities can be used in the classroom to support constructivist learning

# data[].attributes.subject
Many activities can be used in the classroom to support constructivist learning

# data[].attributes.body
o   Discussions

o   Field Trips

o   Experiments

o   Learning by Teaching

o   Problem Solving

# data[].attributes.body
Students will be placed in heterogenous groups in respect to their academic skills. They will be working on composition of transformations. There will be four rounds since each task will have four parts that need to be completed. Each group will complete one part of each task at every round. Students will have instructions for each round at each station. During rounds 2-3, students will be working off of another group’s work. The teacher will call time when it is time for the next round and students will carousel or transition counterclockwise to the next station. The objective of the lesson is for students to perform several compositions and conclude with the single transformation that is equivalent to the composition of transformations. The sociocultural theory is being used by having students work in groups. The constructivist theory is being used by the students with more advanced academics teaching and assisting their group members. Students are problem solving and engaging in discussions. They are working off of each other's work and setting up for the next group.

# data[].attributes.body
Students will demonstrate their knowledge of limits, graphing, and exact trig limits evaluated using substitution. The students will play a game in which they evaluate their own knowledge of problems in the unit, as well as the teacher evaluation the mastery of the problems in the unit. The students receive immediate feedback on their own work and review while the teacher works the problems correcting any errors or misconceptions that the student had while working the problem. This lesson gives the student a power review of the concepts in the unit because the timing is determined by the teacher. All students are engaged and focused while playing this game. Giving students access to the PowerPoint of the game after the lesson provides a good study tool for the students.

Each student will be given five cards with one letter on each card.  The letters are:  A, B, C, D, and E.  Students hold these cards facing themselves protecting the privacy of their choice.

A problem will be presented on the whiteboard.  The students will select their response and puts it on the top of the stack facing them.  The teacher determines the appropriate amount of time to answer the question and then says, “one, two, three, show me”.  The students simultaneously show their choice by turning the stack of cards, with the answer on the front, towards the teacher.

If a student has the correct answer, they rotate forward (unless they are in the first seat of the row, which in that case they will move to the last seat of the next row).  If a person does not have the correct answer they will remain in their seat.  The student with the correct answer would go around any students with an incorrect answer.

The object of the game is to travel around the room and the first person to reach their original seat is the winner.

The teacher works the problem for all to see, identifying any misunderstandings, before proceeding to the next problem.

# data[].attributes.headline
Cup Activity- Writing Equations from Data

# data[].attributes.subject
Cup Activity- Writing Equations from Data

# data[].attributes.body
In this lab activity, students will work in heterogeneous groups to develop a true understanding of slope as a rate of change. Students will be active and involved and must use higher order thinking skills in order to answer questions. Students will work through an activity, measuring heights of cups that are stacked. Students will then determine a "rate of change - slope". Students will be then asked to put this into slope-intercept form. The important part here is in their determining the y-intercept of the equation. Students then take this further and finally attempt to create a linear inequality to determine how many cups, stacked vertically, will fit under a table. Groups will then take turns sharing their equations with the rest of the class.