- Steven G. Krantz, How to Teach Mathematics, Preface
- Daniel Collins, Emral Devany
(1) Prerequisite Challenges
- Started with an overview of the book, as some people were just being informed/picking it up today. In future sessions we’ll plan to cover the main chapters, and try to find ways to attract more attendees.
- Discussed challenges in classes where many students don’t have the expected prerequisite math skills. (For example: Integrated Seminar in Biology, including majors and practicing nurses).
- Examples: Estimated 1/3 may not be able to compute a percent increase between two numbers (or its inverse). This would be used in a metabolism problem, etc. Note that this was previously tested on the CUNY-wide remedial CEAFE (CUNY Elematary Algebra Final Exam), but was recently removed as it was considered too difficult.
- Unfamiliarity with efficient conversion methods: Biology, using the metric units (multiplying by 1000 vs. moving point 3 places). Statistics, converting percent to decimal (dividing by 100 vs moving point 2 places).
- Problems with students knowing algebra but not arithmetic. (CUNY entry testing with COMPASS aborted testing on arithmetic if algebra was passed; this may be reversed with new Accu-Placer test, which combines both in a single test/score).
- Students passing math via raw, herculean memorization of procedures (much harder). Understanding concepts can make these methods trivial to remember.
- Problem of instructor not realizing basic things that students don’t know, possibly for many semesters or years (e.g., types of energy, conversions, checking solutions to equations).
- History of repeating definitions without quantitative applications in some prior science classes.
(2) Testing and Time
- Test-taking history, where students are mostly exposed to multiple-choice tests and tricks to pass them (Krantz in Ch. 2 strongly recommends non-multiple-choice tests for this reason).
- Need to test/quiz on exactly the basic skills practiced in class (not more exotic extensions).
- But: Time constraints on grading, plus assignments, may bias towards multiple-choice tests.
- Suggest: Tests that are part multiple-choice, part short answer (possibly fewer in larger classes).
- Suggestion: Using a point-and-click Rubric in Blackboard for quickly grading assignments and providing feedback (e.g. in a programming course).
- Krantz in Ch. 1: Time management in class: How to avoid an activity that goes long, cut off in middle by end of session, need to pick up in middle next time?
- Prepare 2-3 short exercises in class so one or more can be cut for time if needed.
- Permitting students to go early if they complete exercise quickly: Can give extra attention for other students (with reduced anxiety over struggles in front of peers).
(3) K-3 Experience
- Current student experience in K-6: 1st grade — Test correct performance on several defined procedures. 2nd grade — Give credit for any generation of correct answer, no matter how. Instruction on “how to take multiple-choice test” tricks. 3rd grade — Standardized multiple-choice tests begin, used to assess schools. Seemingly large strategic shift at the point when school needs high grades on standardized tests.
- Common Core complaints: Often unjustified.
- College students not knowing 2nd-3rd grade concepts (scientific method, etc.)
- Passing all students K-12 (no hold backs).