MATH 310: Patterns & Structures in Mathematics

SELF-CHECK

Each week, 🔴Red is a self-check of the previous Rainbow’s Individual Practice. Students are given a PDF of “Featured Responses” but are then required to choose one problem from their original work to improve based on the FRs. They have to upload a screenshot of the original work, a screenshot of updated work, and to write a summary of the changes they made and why.

CONTENT GOALS

• After each Rainbow is due, students have access to a self-check and then have Content Goal assessments (in a form similar to Individual Work) which are untimed and open resource–the main restriction is that they can’t talk to anyone about the exact problems on the assessment or problems with the same numbers. 

• There are 1-3 CGs each Rainbow, 7 per unit, 21 total over the semester.

• Most students will not earn the CG on the first draft–mastery shouldn’t be expected right after learning something! Students receive feedback on an individualized Google sheet, and later there is a 2nd attempt at the same goals with slightly different problems. Students need not attempt any CGs they have already achieved.

• The “Final” is all 21 CGs open for three days - students only need attempt CGs they have not achieved. Students happy with their grade don’t need to do any! Completing CGs can only bring a grade up.

New this semester is grading on a 0-3 scale. This is because students were frustrated with Content Goals being all or nothing. I think it still needs adjustments, but it did resolve a lot of student anxiety.

0 - nothing of mathematical value

1 - there was some mathematics of relevance

2 - Correct solution with work but without thorough explanation; thorough explanation but missing part of the problem

3 - Correct (unrelated arithmetic errors aside) with thorough explanation.

By far, the biggest change this term is that instead of paying for a textbook, students purchased a mathematics manipulative set. I shifted all content demonstration to be from articles available in JSTOR, practitioner articles and videos, and my own writing, diagrams, and videos. This enabled students to spend less money and also have better tools.

I remade nearly all of my videos using a document camera and the manipulatives from the kit so that students could see their use. I had previously used digital manipulatives (and still make them available and use them sometimes), but since the content is so challenging, representations and abstractions were too far out of reach for many students. Working with the same tools they will use with their students both gave them a sense of how to use them with children and also helped them better understand the mathematical concepts.

Accessibility & UDL