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Constructivism is actually really important for math education. In a traditional math ed classroom students are given facts and equations that they are expected to memorize and then regurgitate. With a constructivism approach however, students explore the content and really work at making it concrete in their heads. They commit the information to their long-term memory and then are able to scaffold on it.

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In a geometry class students could learn how to draw basic blueprints of buildings and learn how to scale the measurements. They could then take this knowledge of shapes and measuring to help build houses with habitat for humanity as part of an end of the year service learning project.

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jigsaw is great for math! The students will be put in groups to learn how to expand an equation that is assigned to them at the beginning of the lesson so they will come up with their own method of expanding the equation and then they will split into expert groups and share their method of how to expand. The worksheet attached is what they will use to do this.

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Attached is a website that explains reciprocal teaching, has a lesson plan, and has a worksheet for students to fill out while they go through the lesson is their groups. It has vocabulary for the students to discuss and it promotes conversation amongst their groups.

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Reciprocal Teaching is a reading strategy that is based on student and teacher dialogue. Teachers and students take turns leading the discussions, where the teacher initiates the dialogue and then this responsibility moves to the students.This strategy is comprised of four components: summarizing, questioning, clarifying and predicting.

Teacher or student clarifies challenging aspects of the text to try and help others understand.For example, one might ask, "This was confusing to me, can anyone explain?"

Purpose of the strategy:

The purpose of the strategy in the context of this lesson (next page) is to help students read mathematics definitions and help them translate these definitions into real-life applications. Students are able to have open dialogue with each other and with the teacher to form anunderstanding of math vocabulary terms, and then take this knowledge and apply it to math problems and real-life applications. In this specific lesson, students are presented with definitions of geometric transformations: translations, reflections and rotations.They are askedto discuss the terminology with one another, individually make picture representations ofthese definitions, and conclude with making real-world connections.
Reciprocal Teaching Lesson Plan
This lesson would be taught to an 8 grade Math class.The lesson is made for the beginning of the unit to introduce students to translations and dilations.Students will use prior knowledge and make real-life connections to reinforce reading strategies that have been used in prior lessons.Reciprocal teaching will be used to help students discover their prior knowledge oftranslations and dilations, help each other clarify the meanings of each and predict what real-life connections can be made.

Title: Reciprocal Teaching

8.G.1 - verify experimentally the properties of rotations, reflections and translations

8.G.2 - understand that a two-dimensional figure is congruent to another if the second canbe obtained from the first by a sequence of translations, reflections or rotations

Objectives:Students will be able to...

The purpose of this lesson is to help students understand the meaning of translations, reflections and rotations in utilizing the Reciprocal Teaching reading strategy. Students will be prompted to use prior knowledge to make real-life connections with these new vocabularyterms.

Assessment:

The assessment will consist of completion of written paragraph and active participation in class discussions.

"Reciprocal Teaching": 25 minutes

Clarifying:Identify confusing points - ask students questions such as "This was confusing to me, can anyone explain?"

"Real-Life Applications": 15 minutes

Watch YouTube clip Motion Geometry: Rotations, Reflections and Translations

Student Accommodations:

For students who do not understand the Reciprocal Teaching strategies, teachers should bring to the back of the classroom or the hall during the YouTube clip and further clarify the definitions of teach transformation.Some students may find this reading strategy difficult sinceit is a student-lead class, thus a smaller group of organized teacher instruction will help those students who are having difficulty. Give these students the YouTube clip link to either watch athome, during study hall, or during free time another day.

YouTube clip: Motion Geometry: Rotations, Reflections and Translations
Reciprocal Teaching:Transformations Handout
The word transform means "to change." In geometry, a transformation changes the position of a shape on a coordinate plane. What this really means is that a shape is moving from one place to another. The properties of transformations are the same: the images of the original figure are congruent.

There are three basic transformations: Translations, Reflections and Rotations.

Translations are transformations which shift all points on the coordinate plane in the same direction and in the same distance. The translation of a figure is congruent to the original figure. Every point in the figure slides the same distance in the same direction. It's like taking a step or steps forward, backward or sideways. (slide)

Reflections are transformations that flip a figure across a line and face the opposite direction. The reflection of a figure is congruent to the original figure. This is a reverse image. Think of what you see when you look in a mirror. The points on the reflection image are the same distance from the line as the original image points. (flip)

Rotations are transformations that turn a figure about a fixed point. The rotation of a figure is congruent to the original figure. Think of the terms clockwise and counterclockwise. The figure is turned from the original image. (turn)

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Reciprocal Teaching: 8th Grade Math - Language, Literacy and Culture Spring 2012

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Reciprocal Teaching is a reading strategy that is based on student and teacher dialogue. Teachers and students take turns leading the discussions, where the teacher initiates the dialogue and then this responsibility moves to the students.This strategy is comprised of four components: summarizing, questioning, clarifying and predicting.

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The attached website explains how we can use math equations as prompts for inquiry learning. You could use any equation for any section and use this method. It allows the students to explore the equation on their own and come up with their own conclusions.

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Inquiry Maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). The website has resources for secondary school teachers.

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An example for project based learning in math is having students get into groups and find the quadratic equation of famous arches. They would have to look up specifications for there arch for how tall it is and how wide it is to be able to have an accurate equation. They will then present their project with some fun facts about their arch and how they were able to come about finding the quadratic equation for it.