Overview
Test your knowledge of a wide variety of geometric ideas with this quiz tool. Whether you're wanting to test previous knowledge or spur on the exploration of new ideas, this tool provides practice questions ranging from basic calculations to multi-step logic problems.
Curator: Darrell Glover
Brief Description of Tech Tool: This tool is presented in a quiz style, giving the user problems from many different areas in geometry. Use the given information to find the answer, input it, and check the correctness. As the user progresses, the concepts and questions become more difficult and require linking together multiple geometric concepts to solve the problems.
Technical & Cost considerations: This tool is free to use from the popular Math Playground website. It utilizes Adobe Flash Player and should work on any computer with an internet connection.
Evaluation
Description of Learning Activity
This tech tool can be used in a variety of ways. A teacher can have it projected for whole class use to practice and discuss problems together or students can use it to practice by themselves or in small groups. With the wide variety of geometry questions that are asked, if an unknown concept is encountered, it could spur on discussion (in a class setting) or exploration of the new concept (in a private setting).
1. Learning Activity Types
- LA-Practice - this tool presents geometry problems involving shapes and angles for the user to solve.
- LA-Explore - due to the wide range of questions asked and depending on when the tool is used in a geometry curriculum, unknown ideas may be encountered, encouraging the exploration/investigation of new mathematical ideas.
2. What mathematics is being learned?
Standards
NCTM:
- Analyze properties and determine attributes of two- and three-dimensional objects
- Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them
- Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others
- Use trigonometric relationships to determine lengths and angle measures
- Use various representations to help understand the effects of simple transformations and their compositions
Common Core (non-specific):
- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Prove geometric theorems
- Define trigonometric ratios and solve problems involving right triangles
- Understand and apply theorems about circles
- Explain volume formulas and use them to solve problems
Proficiency Strands
- conceptual understanding - some questions give limited information, requiring an ability to pull together multiple concepts in order to solve a problem.
- procedural fluency - the repetitiveness of some question types (if the tool is used multiple times) builds fluency in the procedures needed to solve the problems.
- strategic competence - many of the advanced questions require linking multiple geometric ideas together in order to find the answer.
- adaptive reasoning - like strategic competence, the need to link ideas together means some of the more advanced questions can be solved in different ways.
3. How is the mathematics represented?
The mathematics in this tool is represented both numerically and symbolically. The problems mostly consist of drawings with certain labelled information that must be used to find the answer. Because of this, the tool itself is quite simple.
4. What role does technology play?
The main advantage that this tool provides is wide variety of geometry ideas that are touched on. The more advanced questions definitely test the user's ability to link many concepts together to find the answers. One notable disadvantage is the quiz format; the user doesn't get to manipulate or change the values or problems, therefore, it is much more of a knowledge testing tool than a knowledge expanding tool.
Affordances of Technology for Supporting Learning
- Computing & Automating - the tool automates the checking of the input answers.
- Representing Ideas & Thinking - the tool represents a multitude of geometric ideas in the presented problems.
5. How does the technology fit or interact with the social context of learning?
This tool is more suited towards individual use however, it can be used for whole class or small group use/discussion. Whole class or small group use would be good for the more advanced questions where multiple steps might be needed to arrive at the correct answer.
6. Additional Comments
While this tool is neat overall and has some good application, there are a limited number and type of questions. The quiz is only 20 questions long before it must be restarted. Once restarted, the user will notice that the type of questions asked are virtually identical (in some cases exactly identical) only with slightly different numbers (although in some cases, with the same numbers as well). This is especially true with the questions in the higher levels where the questions asked are the same ones almost every time. In addition, there is nothing available to explain the math behind the answers. While the tool will give the user the correct answer if a wrong one is entered, the tool does not explain how to solve the problem. For some, this will encourage the user to research how to solve such problems but, for others, it may be discouraging.