Reading Apprenticeship Inspired Assignment or Lesson

Salvador Guerrero, Discrete Math, Investigating Boolean Algebras

Purpose

Students will explore the topic of Boolean Algebras by completing the project in groups and then reading the (OER) textbook. This activity is to be completed near the end of the course (it will take the place of an exam) and will help students to see a concrete application of an abstract topic. Students will further develop their agency in learning as this final project will be completed without any prior lectures on the topic, i.e. students are entirely responsible for their learning (earlier projects will be assigned after an introduction/lecture). In comparing their work for the project with the work in the textbook students will improve their metacognition by re-visiting content learned from the project as they work through the textbook assignment.

Context

This activity will take place during the final third of the quarter and students will have already developed a good understanding of elementary set theory and logic. Moreover, students will have attained the mathematical maturity to complete the assignment as we will have already covered (unrelated) abstract and applied topics including combinatorics, functions, relations, and graph theory. Throughout the quarter students will have been guided to making connections to prior knowledge and to ask questions about how that prior knowledge may be expanded on. Moreover, students will have submitted corrections to various assignments so they will be familiar with the process of analyzing their own work and thought process. Finally, students will have practiced working in groups and questioning the text since the first week of class; in particular, students will have read and discussed in groups on a weekly basis.

Criteria

Student work will be evaluated for completeness and correctness; each group will exchange a rough draft with another group and they will offer suggestions as to what may need changes. Students are expected to participate with their groups and are expected to show that they have – either by meeting in class or by meeting outside of class (or via zoom) and recording their collaboration (google, or similar cloud, collaboration is also acceptable). Lastly, each group will meet with instructor to present their final draft and each student’s contribution to the discussion will be evaluated for consistency with group results (or clear explanation of any inconsistency).

Metacognitive Conversations

Students will read text and discuss with group and they will analyze the work of another group.

Details

This activity is a real time activity taking up a minimum of one week through the rough draft, plus an additional weekend for the final draft. Reading of the text and comparing understanding to that from project will take up the following week.

Complete the project, making sure to all notes and scratch work as an appendix to final draft.

Day 1 – read through the entire project and discuss with your group

Day 2 – continue discussion with group and determine how to complete the exercises in the project

Day 3-4 – collaborate to complete the exercises

Day 5 – exchange rough draft with another group

Weekend – complete final draft

Day 6-8 – read text in groups and complete assigned problem sets. Discuss how understanding of project helps to motivate reading and how reading expands on project.

Day 9-10 – meet with instructor to present final draft

Text and Materials

Students will read from Applied Discrete Structures by Ken Levasseur, Chapter 13 (p.348-367) and complete Applications of Boolean Algebra: Claude Shannon and Circuit Design by Janet Barnett