Flipped classroom, what a tempting concept! But this suppose before class reading.
My first trials where not successful and couldn't be: I just asked the students to read this or that section in their book or look at this or that online resource. No guidance, no reading question/quiz. Students just came to class saying: "I tried, miss! But I didn't understood..." And I ended up lecturing. How worst can it be?
The most recent ones went better, thanks to few reading questions, always including Mazur's last question: “Please tell me what you found difficult or confusing in this reading assignment. If you did not find anything difficult or confusing, tell me what you found most interesting.”
Still, I just tried it on some particular topics, having difficulties to "let go" and not lecture on difficult or completely new concepts. Why? I think mainly because I do not trust students reading capacities. In chapter 9, Bean gives many reason why students have difficulties to read. Two points kept my attention:
The most recent ones went better, thanks to few reading questions, always including Mazur's last question: “Please tell me what you found difficult or confusing in this reading assignment. If you did not find anything difficult or confusing, tell me what you found most interesting.”
Still, I just tried it on some particular topics, having difficulties to "let go" and not lecture on difficult or completely new concepts. Why? I think mainly because I do not trust students reading capacities. In chapter 9, Bean gives many reason why students have difficulties to read. Two points kept my attention:
- "A School culture that rewards surface reading", encouraging surface reading and short-term memorization rather than deep learning.
- "Students' resistance to the time-on-task required for deep reading".
(Experts) hold confusing passages in mental suspension, having faith that later parts to the text may clarify earlier parts. They "nutshell" passages as they proceed, often writing gist statement in the margins. They read a difficult text a second and a third time (...) They interact with the text.
A reading guide?
Now I think the key for successful pre-class reading lies in 2 types of guidance. One specific to the particular reading through reading questions – Which is what I already started with last term. But also a more general one giving students guidelines for a good reading. Luckily for me, Derek Bruff shared his "Tips for Reading Your Mathematics Textbook". They are totaly in line with many advises given by Bean in the second part of chapter 9. So I just made some minor changes (my additions in blue).
- Read the preface of your textbook. There’s usually advice there for students about reading the textbook that addresses features of your particular textbook.
- Read the narrative of each section. Most sections’ narratives are designed to be read from beginning to end. The examples, in particular, are supposed to illustrate ideas and make them concrete – not just serve as templates for homework exercises.
- Read the pictures. The pictures in your textbook are not “illustrations” or “decorations.” Pictures are everywhere in your book, sometimes even in the middle of sentences. That’s intentional: graphs are an important part of the language of calculus.
- Pay careful attention to vocabulary. Mathematics is not a natural language like English or French, but it has its own vocabulary and usage rules. Words like theorem, rate, amount, concave, and stationary point have precise, agreed-upon mathematical meanings. Understanding such words goes a long way toward understanding the mathematics they convey; misunderstanding the words leads inevitably to confusion.
- Read with pencil and paper handy. Sure, you believe your textbook, but check the work you see there anyway. You don’t learn difficult material just by reading a nice presentation of the material – you need to break out pencil and paper and convince yourself that you follow the reasoning and computations. You might even try to work out examples before looking at their solutions in the textbook.
- Don’t bother highlighting, use the margins. Math textbooks generally use page layout, fonts, and colors very well to organize information. There’s usually little use in highlighting or underlining your textbook yourself. Instead, every time you feel the urge to highlight or underline something, write out in margins why you wanted to underline it. Use the margins to summarize, ask questions...
- Read before class. For new material, expect not being able to grasp everything right away. Keep confusing passages in mental suspension: later part of the text may clarify. When reading your textbook before class, write down a few questions you would like to see answered in class. Make sure to get them answered in class.
- Be efficient when taking notes. By reading your textbook before class, you won’t have to take as many notes in class since you’ll know what definitions, theorems, and examples are already available in your textbook. Saltzman and Coffin write, “Since you have already paid for an expensive printed copy of the material, there is no need to acquire a hastily hand-written copy as well.”
- Read after class. Identify concepts and examples that are still unclear, and look to your textbook for clarification. As you work on your homework, refer to your textbook for explanations and useful examples.
- Read and re-read. Keep re-reading (either before or after class) until understanding is gained. Sometimes read linearly through the material, other times skip around trying to follow your own thoughts.
References and further readings
- J. Bean, Engaging Ideas: The Professor's Guide to Integrating Writing, Critical Thinking, and Active Learning in the Classroom (2011).
- Derek Bruff's blog: Agile Learning.
- M. Saltzman & M. Coffin, How to Survive Your College Math Class (1998)