Rubric Assignment 11: due Nov. 19John T. BaldwinNovember 26, 2007Rubric-Geometry to AlgebraThe assignment was to correct the argument for the distributive law asassigned in HW 9 (due Nov 5).I am revising the rubric that was used for the first ass ignment. A numberof people got much closer but stumbled at the same point: see 4) below. Anumber of people did not turn it in. I will accept a late paper as this is a veryimportant topic.This is the grading rubric for the assignment due Nov. 5. It is Homework 9on the website.The problem gave a definition of ‘multiplication’ ⊗ and ‘addition’ ⊕ of equiv-alence classes of line segments. The assignment was to prove that ⊕ is commu-tative, ⊗ is associative, and ⊗ distributes over ⊕. There were no numbers inthe problem; no numbers should appear anywhere in the proof.The following rubric categorizes the response. For almost all students, onecategory applies to the paper as whole. A few students did markedly differ-ent work on different problems and this is reflected in the marking. A majordifficulty for a few p e ople was lack of words. Proofs are written in English.Diagrams can illustrate but not replace a proof.1. There was no indication of understanding the roles of algebra and geom-etry in the problem.2. The response partially uses geometric arguments but eventually falls intothinking that length has bee n defined and one can manipulate numbers.3. The geometric idea is understand pretty well but there are technical prob-lems in the proof or it is not prop erly explained.4. In carrying out the geometrical argument, there is an unnecessary (andincorrect) appeal to the notion of proportionality for numbers. In thisframework, this notion has not bee n defined. But the rest of the argumentis correct.5. The geometrical arguments are carried out to solve the problem.1Nov. 26. A score of 1-5 was recorded for the problem on the distributivelaw. Those who had it correct the first time were given credit again.Nov. 12: I have recorded these scores not as part of your grade but to tellme where the class is. I did however as part of the grade record those peoplewho made a good faith