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Finding Polynomial Roots

by Dan McKinney 3 years, 9 months ago


We would like feedback on our roadmap.

Thank you,

Dan and Katie


Elliot Soloway 3 years, 9 months ago

Comments on Roadmap: States of Matter

Submitted by: Daniel McKinney, Kathryn Wippel

Reviewed by: Cathie Norris & Elliot Soloway, 12/27/18


1. This lesson brings a lot of information together in ONE PLACE, e.g., the different methods for solving for a root, background information about what a root is, etc. Perhaps that should be pointed out in the Teacher Narrative node? 
2. Indeed, this lesson might well be a model for other math (other subjects?) lessons: initially provide background information – using multiple media (text, video) – and then include all the information needed for a complete “conceptual chunk” – e.g., ways to solve for real roots.
Here are more detailed comments:
3. In the definition of the Root document, there is a question at the end. Is the student expected to provide the answer? How will it be graded? How will the student know if he/she is right/wrong? 
4. The instructions in the “How many roots are there?” are: “Watch the video to understand how many roots exist for your polynomial.” What is meant by “your polynomial”? Does each student have a polynomial? 
5. The video in the How many roots” node is entitled: “The Fundamental theorem of Algebra” – we were confused. We were expecting a video about roots. The video about roots comes later in the video in fact. The learner needs to be patient, watch from the start, and then learn about the roots. Perhaps explaining what the learner is about to see might address this confusion. 
6. In the instructions for the activity “Multiplicity of Roots” should the learner answer the “check understanding” questions on the website? If so, perhaps that requirement should be made explicit?
7. The Instruction tabs for the 3 methods are currently empty.
8. Might it be useful to provide a link to an online graphing calculator? While there are several (e.g., Desmos - or ) – learning how to use the online graphing calculator is not easy! 
9. In fact, the Google Doc in “solve by graphing” refers to the Desmos calculator! 
10. The Google doc for Solve by Factoring is empty.
11. How is the notion of a “real root” and a “rational/irrational” root related? Does that need to be explained in the lesson? How much “background” knowledge needs to be provided? Good question!
12. There are 3 ways to solve for real roots. Under what circumstances would each method be used? 
13. In the “solve by graphing” activity, the student is asked to solve 1 problem. Is there an expectation that the student will practice solving more problems? 
14. The “Legend” was very useful – the nodes were color coded according to their role, their function. 
15. Unfortunately, the “Driving Question” node doesn’t provide a tab for instructions. It might be useful to choose a different node, but include instructions. For example, in the “finding the real roots” node, it might be useful to be explicit and tell the learner: if you already know about real roots, jump down to learn about “ways to solve for real roots.” (Perhaps WE should simply add a tab in that “cloud shaped node” – it would be simple enough. Consider it done – we WILL put a tab for instructions in the Driving Question node. Thank you for the inspiration!)