Mixed Reality
Solid Figures.
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The Net Method for understanding surface area of solid figures.
Image copyright © 2005, 2020 - OnlineMathLearning.com
Instructional Design for Mixed Reality: a sample project
1. Analysis
- Context and learners
Santa Fe College’s Adult Education program serves 700-800 students annually at three different campuses: our main campus in northwest Gainesville, our downtown Gainesville campus, and our Archer campus. The bulk of our staff and resources are located at the northwest campus, with only a few staff at each of our downtown and Archer campuses. Students join our program seeking English language skills, high school equivalency (GED), and/or entry into college classes or a vocational program. According to 2018/19 National Reporting System data:
· 55% of our students are classified ABE, Adult Basic Education (0-8.9 Grade Level Skills)
· 39% are English for Speakers of Other Languages (ESOL) students
· 7% are GED Prep level (9th Grade Level Skills and above)
· Predominant ages 25-44
· Predominant demographic groups include Hispanic and African American females
· 42% are unemployed at program entry (Falt, 2019).
- Need assessment
Though widely diverse in their background, goals, and abilities, the Adult Ed students that I work with most closely are generally seeking to address normative needs: to either pass the GED test or to achieve high enough test scores on the Test of Adult Basic Education, or TABE, to qualify for admission into a vocational program. I am also working from my own (and that of some of my fellow math instructors’) felt needs that many of our students have particular difficulties with some aspects of geometry.
2. Purpose and instructional goals
- Significance and rationale for using MR
The purpose of this project is to boost student achievement in the geometry of solid figures in order to improve their scores on the GED and TABE tests. Solid figures are three-dimensional objects such as cubes, rectangular prisms, triangular prisms, cylinders, and cones. In conventional geometry instruction, all lessons and instructional materials take place in two dimensions. Many students are able to easily calculate characteristics of two-dimensional shapes such as area and perimeter when viewing them on paper or the computer screen. However, most students have difficulties grasping concepts such as volume and surface area because doing so now requires them to understand shapes in three dimensions. MR/3D will offer me greater means of representing solid figures and allow students more means of engaging with these figures. Students will be able to manipulate each figure, examining it from multiple perspectives, counting the total number of sides and noting the shape of each. Using MR/3D, students will also be able to “explode” each figure and use the net method to calculate the surface area. This method can help make the standard formulas for surface area less abstract; for example, displaying that the surfaces of a triangular prism are comprised of two triangles and three rectangles.
- Measurable instructional objectives
My goal is that each student be able to understand and correctly calculate surface area for a variety of solid figures. More specifically, upon completion of my geometry module:
· Each Adult Ed student will correctly identify 80% of the most common solid figures on an end-of-unit quiz.
· Each Adult Ed student will correctly match 80% of the most common solid figures to their corresponding surface area formula on an end-of-unit quiz.
· Each Adult Ed student will correctly calculate the surface area for 75% of the solid figures presented on an end-of-unit quiz.
· Each Adult Ed student will correctly infer missing values (e.g., height) when the surface area is provided for 70% of the solid figures presented on an end-of-unit quiz.
3. Content
- Describe the unit content supported by MR
The unit content consists of a variety of solid figures, as listed above. Students will learn to identify the objects based on their characteristics. Utilizing the net method to familiarize the students with each figure’s constituent parts, students will better understand the logical basis for the derivation of each figure’s surface area formula. Once familiar with these formulas, students will calculate surface area using both the provided formula and the net method. Finally, when provided with the surface area and all but one of the measurements for a given figure, students will learn how to work backward from the surface area formula to determine the missing value. This learning will take place in a Canvas-based online module that students can use in the classroom on an appropriate MR device.
- Develop a 3D model that will be used to support instruction. Upload the 3D model file (.stl or .obj) to Canvas and ePortfolio. You can either use a Sense 3D scanner for creating the 3D model or the Tinkercad.com platform.
The MR/3D models, developed via Tinkercad, will also be used to create physical 3D objects that the students can handle in the classroom. These physical objects will be “hinged,” allowing them to be unfolded so that students can see a physical representation of the net method for calculating the surface area of solid figures. Here is a link to a Zspace studioactivity file for a very simple geometry lesson that I created just to experiment a bit. I harvested the basic shapes used in the lesson from Tinkercad, then created the lesson in Zspace. Here are a few additional OBJ files that were relevant to this project: (1) components of a rectangular prism, (2) components of a right triangular prism, and (3) breakaway hinges affixed to matching rectangles.
4. Instructional Strategies
- Delivery format/device: Identify MR device that will be used to support instruction
This module will be housed in the course’s Canvas shell. However, due to the prohibitive cost of zSpace equipment, it is unlikely that this specific lesson will be actively used except with borrowed equipment during a very small window of time. I anticipate instructing the students in the basic use of zSpace equipment, then opening the geometry module for their use. My goal would be to work through the entire lesson over the course of two class periods.
- Teaching methods
Students will be introduced to the concept of solid figures and how these figures differ from the two-dimensional shapes that they have gotten used to working with. The characteristics of each figure will be described using both illustrations and the 3D models. After gaining familiarity with the zSpace equipment, students would then work from their notes to identify the types of solid figures presented to them. Students would be encouraged to examine each shape in three-dimensions, using the zSpace equipment and/or 3D models. Next, students would be instructed in how to “explode” each object in order to identify its constituent parts and measurements, and would link this part of the lesson to familiarizing themselves with each figure’s surface area formula. Finally, a diversity of solid figures of varying measure would be presented to the students in order to practice calculating surface area as well as calculating missing dimensions when surface area is provided.
5. Assessment of learning outcomes
- Formative
Formative assessment for this lesson will consist of a series of practice problems. Students will receive instant feedback upon completing each problem thereby allowing rapid intervention if the students are struggling with the concepts and/or the equipment.
- Summative
Summative assessment will consist of an end-of-unit quiz that will offer a variety of surface area-related questions in two-dimensions. The summative assessment will be in two dimensions because this mirrors the testing environment (TABE and GED) where the students will ultimately have to demonstrate mastery. Students must show the ability to extend what they have learned in three dimensions back to the two-dimensional realm. My hope is that they will now be better equipped to visualize the solid figures due to their experiences working with them using zSpace and/or the 3D models.
6. Follow-up Research
Analyze available follow-up research strategies/design/methods/techniques for evaluating the instructional impact of MR based learning and 3D modeling.
In order to truly ascertain the effectiveness of the MR/3D intervention, it will need to be compared with other possible approaches. A control group (no intervention and/or standard teaching methods only) could be used. Additionally, and particularly since acquiring zSpace equipment presents some challenges, an additional option would be to test the use of 3D physical models only without the use of zSpace equipment. If these models are shown to be just as effective in helping the students to visualize solid figures, it would save considerable time and expense. The 3D models present an additional advantage for students who are vision-impaired as compared with the zSpace equipment, another reason to scale the lesson design down if the 3D models are shown to be just as effective.
References:
· Falt, J. (2019). Retrieved March 25, 2021, from National Reporting System for Adult Education.
Header photo by CHUTTERSNAP on Unsplash