Overview of Lesson Four - A Garden of Learning
Problem-based Learning is where students take a role in the discovery of a concept by exploring real life situations. In ‘A Garden of Learning’, students will use learn about the measurement and construction of geometric shapes by designing a garden for an imaginary client. Students will then evaluate their peer’s projects and choose the best one for the client.
Resources and Preparation
This online lesson will help students discover how to construct geometric shapes by exploring a landscaping project. The target audience is pre-college level mathematics students, middle school and high school students. The lesson would take the instructor about 5 hours of research and utilize the following resources:
GeoGebra
Sacred Garden
Geometric
Screencast-O-Matic
Auntsallyslearning wiki
Website platform of your choice
GeoGebra
Sacred Garden
Geometric
Screencast-O-Matic
Auntsallyslearning wiki
Website platform of your choice
Theory to Practice
One hundred years ago, students learned exactly what their instructors wanted them to know by lecture and was required to give back their understanding of the concept by some measurement of understanding. There were those students who excelled at it and some who struggle with it. Learning styles can be a deterrent to understanding. The eMINTS (enhancing Missouri’s Instructional Networked Teaching Strategies) institute says, “Students understand more when they actively construct meaning in response to questions and challenges. This philosophy contrasts with the traditional notion that students absorb information passively. Students do not come to understand concepts and principles by passively taking in information.”(pg.5)
There are two basic modes of thought regarding the teaching of mathematics to students.The first mode, Skemp (1976) says, is a more traditional approach of classroom lecture and drill called instrumental learning. In this approach, the instructor gives content by standing in front of the class lecturing, and then measures the content the student has acquired by a test or quiz. He also mentions a second way as a more organic way of discovery called relational learning. In this mode, the student learns concepts by solving real life or inquiry- based problems. This type of learning allows the student to explore the theorems and context of the concept.
This is the essence of problem-based learning.
There are two basic modes of thought regarding the teaching of mathematics to students.The first mode, Skemp (1976) says, is a more traditional approach of classroom lecture and drill called instrumental learning. In this approach, the instructor gives content by standing in front of the class lecturing, and then measures the content the student has acquired by a test or quiz. He also mentions a second way as a more organic way of discovery called relational learning. In this mode, the student learns concepts by solving real life or inquiry- based problems. This type of learning allows the student to explore the theorems and context of the concept.
This is the essence of problem-based learning.
Standards
Common Core Standards
Apply geometric concepts in modeling situations
G-MG 3- Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost;
working with typographic grid systems based on ratios).
N-Q1- 1. Use units as a way to understand problems and to guide the solution
of multi-step problems; choose and interpret units consistently in
formulas; choose and interpret the scale and the origin in graphs and
data displays.
Indiana Mathematical Standards
MA.G.8.4 2000 Geometry Students deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems
College Board
MI.3.
Student distinguishes between length and area contexts, develops an understanding of formulas, and applies them to find the perimeter/circumference and area of triangles, quadrilaterals, circles, and composite figures made from these shapes.
Apply geometric concepts in modeling situations
G-MG 3- Apply geometric methods to solve design problems (e.g., designing
an object or structure to satisfy physical constraints or minimize cost;
working with typographic grid systems based on ratios).
N-Q1- 1. Use units as a way to understand problems and to guide the solution
of multi-step problems; choose and interpret units consistently in
formulas; choose and interpret the scale and the origin in graphs and
data displays.
Indiana Mathematical Standards
MA.G.8.4 2000 Geometry Students deepen their understanding of plane and solid geometric shapes and properties by constructing shapes that meet given conditions, by identifying attributes of shapes, and by applying geometric concepts to solve problems
College Board
MI.3.
Student distinguishes between length and area contexts, develops an understanding of formulas, and applies them to find the perimeter/circumference and area of triangles, quadrilaterals, circles, and composite figures made from these shapes.
Objective
Upon successful completion of the Garden of Learning unit, the students will:
1. Be able use geometrical concepts to problem solve real life situation
2. Be able to compute units appropriately
1. Be able use geometrical concepts to problem solve real life situation
2. Be able to compute units appropriately
Build Inquiry
Students will visit a local landscaping business and talk to a professional landscaper to find out how landscapers design projects. The emphasis will be on drawing designs. (2 hours)
Students will then watch videos on garden design by visiting auntsallyslearning.weebly.com (15-20 minutes)
Sacred Garden
Geometric
Students will then watch videos on garden design by visiting auntsallyslearning.weebly.com (15-20 minutes)
Sacred Garden
Geometric
Instructional Delivery
Students
will become pretend owners of a landscaping business that has a special client
who wants a garden built and landscaped within a specific dollar amount. This
garden must have at least two separate garden areas and have five different
polygons within the total area, 800 sq. ft. There will be considerations for
ornamental decorations and fencing as well as flowers. The student’s job is to
create the best garden for the dollar restriction of $2500.
The student will have free reign to be creative.
Students should go to auntsallyslearning.weebly.com and work through lesson ‘A Garden of Learning’ and save their work after each section.
First stage-Students will draw the first draft of the shapes of the garden using GeoGebra. (1-2 hours) If students do not have GeoGebra on their computer, they can click on the download GeoGebra link. For an example of the GeoGebra tip sheet click here.
Second stage –Students will pick a fencing option and then determine if they want decorative items in their garden using the Fencing and decorative item table (30 – 45 minutes)
Third stage- The students will determine what flowers to plant flowers using the Flower table (1 hours)
Fourth Stage-Students will draw up the proposal of the garden listing all cost using Garden proposal worksheet. They will also create a 2-3 minute screen cast using Screencast-O-Matic of their garden project in GeoGebra with explanations of how they fulfilled the physical requirements of the client and why their project should be picked. Students will post their screen cast and proposal worksheet on Aunt Sally’s wiki. (30-45 minutes) An example of a design plan and garden proposal is on auntsallyslearning.weebly.com .
After all students have posted their projects, students will vote for the project that they think the client would like the best (excluding their own).
The student will have free reign to be creative.
Students should go to auntsallyslearning.weebly.com and work through lesson ‘A Garden of Learning’ and save their work after each section.
First stage-Students will draw the first draft of the shapes of the garden using GeoGebra. (1-2 hours) If students do not have GeoGebra on their computer, they can click on the download GeoGebra link. For an example of the GeoGebra tip sheet click here.
Second stage –Students will pick a fencing option and then determine if they want decorative items in their garden using the Fencing and decorative item table (30 – 45 minutes)
Third stage- The students will determine what flowers to plant flowers using the Flower table (1 hours)
Fourth Stage-Students will draw up the proposal of the garden listing all cost using Garden proposal worksheet. They will also create a 2-3 minute screen cast using Screencast-O-Matic of their garden project in GeoGebra with explanations of how they fulfilled the physical requirements of the client and why their project should be picked. Students will post their screen cast and proposal worksheet on Aunt Sally’s wiki. (30-45 minutes) An example of a design plan and garden proposal is on auntsallyslearning.weebly.com .
After all students have posted their projects, students will vote for the project that they think the client would like the best (excluding their own).
Assessment
Students will be assessed using a rubric.
Extension
The instructor will find an area around their school or other non-profit organization where the class will design and implement an actual landscaping project.
Citations
eMINTS National Staff (2003). Inquiry-Based Mathematics. Retrieved from
http://www.southtechnical.org/emints/viele/agendas/emints_11/year_two/20c-math.pdf
Skemp, R. R. (1976). Relational understanding and instrumental understanding.
Mathematics Teaching, 77, 20-26.
http://www.southtechnical.org/emints/viele/agendas/emints_11/year_two/20c-math.pdf
Skemp, R. R. (1976). Relational understanding and instrumental understanding.
Mathematics Teaching, 77, 20-26.