|Original CEP Post|
Description of Learning Activity
1. Learning Activity Types
- LA-Practice - practicing for fluency
- This activity is a great way to have students practice writing two column proofs. Students can easily click the "proof" button to check their answers, and monitor how well their proof writing is going. The practice proofs get more difficult and more involved as you progress through the problems, so it can also be used as a leveled practice.
2. What mathematics is being learned
- PS-procedural fluency
- This website provides a total of 10 two-column triangle congruence proofs. Students can work at their own pace through these problems, and can check their answers against the key as they go.
- PS-adaptive reasoning
- Students are constructing mathematical arguments as they write two-column proofs. Students make statements and must be able to justify their statements in order to write a cohesive proof. Students are not told which triangle congruence postulate to use, but must be able to analyze the diagrams and givens to determine how to prove the two triangles are congruent.
Additional comments on what is being learned
3. How is the mathematics represented?
4. What role does technology play?
Affordances of Technology for Supporting Learning
- Computing & Automating -
- Representing Ideas & Thinking - This website provides students with proofs of varying levels of difficulty and students have to visualize which triangle congruence postulates can be used to prove congruent triangles.
- Accessing Information - This website provides students with an answer key for each of the proofs they write. This is immediate access to information and can be very helpful formative data for students.
- Communicating & Collaborating -
- Capturing & Creating -
5. How does the technology fit or interact with the social context of learning?
6. What do teachers and learners need to know?
As mentioned, teachers must monitor student use of the website. The answer keys should not be revealed until students have first written the proofs. Again, students must have the background knowledge of all triangle congruence theorems as well as CPCTC in order to fully engage with this website. The proofs get more difficult, and number 8 and 9 in particular, require some properties that may or may not be covered in you course, so you may choose to skip those. Overall, this is a good website, and a nice way to have students use computers to practice proofs which is traditional simply a pencil and paper activity.
How this Supports & Supplements PBL/PrBL
As I mentioned at the beginning of this post, proofs are a difficult concept to address directly through projects and problems. Students can most certainly practice attending to precision and justifying their statements and claims in projects and problems, but create a direct proof using geometry theorems is a tough subject to master through problems alone. (I say just problems, because I have yet to do a project with proofs, though I frequently run activities and seminars that are problem-based).