The flaws of (some) textbooks

Recently, I was asked "Why do you dislike Textbooks?" and upon reflection, here are the issues I see:

Problem 1: Textbooks assume you need to be taught and shown how to solve a problem before you are given the problem.

This is absurd to me.  When I, and probably most, encounter something I do not know how to do, the first thing I rarely do is look for an instructional video on how to complete the task.

Ironically, the first thing I do is actually play with the problem and see how far I can get without any assistance.  That is right; I play!   This play cannot happen if my hand is being held and shown how to complete the task.  Learners, specifically children, are not afraid to be wrong, take chances, and try to truly problem solve, yet a textbook is designed around the idea that a child loves to be told what to do.

This ruins the fun!!!  I say again, this ruins the fun!  It is comparable to turning on a movie and someone telling you "The main character dies at the end!"; Joy lost!

Problem 2:  Pseudo - context

In almost every textbook I have seen there is always some sort of situation that can only exist in "textbook land", a magical place where the following is true:

Textbooks usually tell students all the information, in the order the need it, and then call it "Problem Solving".  My favourite question and answer was when I read the following question from a textbook:

Jason weighed a fish, and found out that if you took the weight of the fish and added it to half the weight, the result is 20 lbs.  How much does the fish weigh?

The best answer was from a student who exclaimed:

Ask Jason he weighed the damn thing!

Brilliant response to a horrible question!

Problem 3:  They "unitize" learning.

Again, a common problem I see with textbooks, is they assume you need to learn A, then B, then C, to master idea D.  In my experience, creating these disjoint learning situations, or what I call "silos of learning" causes problems for students.  

A common practice in textbooks are "Chapter Tests", which means the pages after these tests have rarely little or nothing to do with the previous pages.  In essence, the learning that happened yesterday will have nothing to do with tomorrow.  

A great practice is to weave essential learning outcomes throughout your entire course.  This contradicts the textbook.  If you feel a certain outcome is important for all to master, I would hope that your students work with that idea throughout the entire course and not just for a finite time (week, or month) and then move on and never relate new learning to previous learning.  

Disclaimer:  Does this mean I don't think textbooks belong in schools?  NO!

This means educators have to be aware of the shortfalls of textbooks.  The biggest idea we always have to remember is that these resources were created, usually in an office, to be sold across an entire continent or country.  They are not designed for "your" kids; or really anyone's kids for that matter.  

Textbooks should be used similar to encyclopedias in the classroom.  Reference material.  If a student is struggling with a concept, give them a textbook, show them a certain page and advise him/her to complete some (not all) questions.  When completed, have a conversation, and then ask him/her to return the textbook to the classroom shelf.

Visualization in Math

5 things I was NOT doing as a Math Teacher... that I wish I did

Recently, I heard a Harvard researcher state,

Sometimes the problem is not in what you are doing, but instead in what you are NOT doing.

This made me reflect upon my first 8 years of teaching math. What was I NOT doing that may have increased learning? If I could go back in time, here are 5 things I wish I did more (or even at all), in no specific order:

• I never gave pictures to students and asked them, "Where should the origin be placed to best understand, or work with, this image?". Instead I would always supply images to my students with a Cartesian coordinate already drawn on. If I could go back, I would make time for students to discuss and debate on where is the "best place" for the origin to be placed on an image to solve the problem given.

• I never explained what "simplify" truly meant. I would give students loads of questions and I would write "simplify" as a directing word. In my classes "simplify" meant: Add, subtract, factor, expand, combine like terms, rationalize denominator, etc. I wish I showed students where, and ultimately why, each form may be simpler than other forms; however, change the question and then a different form may be actually simpler.

• I never asked students to actually measure needed quantities to solve problems. I usually gave students problems with all the information needed, even in the order they needed it, and then asked the question. If I could go back, I would have started asking questions such as "To solve this problem, what would we need to measure and/or determine?". I think it is important that students know how to measure, but more importantly they know what is worth measuring.

• I never allowed students to be individuals, not only in the instruction process, but also the assessment process. Most of my tests required students to learn the required material by the same day, and then even asked my students to demonstrate learning the same way. If I could go back, I would allow students to demonstrate learning when they have mastered the material, regardless of the speed and pace of the other students. In addition, I would also have asked students to relate their learning, when possible, to their passions and interests.

• I never built my course to allow connections to be built between essential learning outcomes. Instead, I built my course in units where I would teach outcomes as disjointed ideas and rarely make connections between each unit; I created silos of learning throughout the year. If I could go back, I would actually remove all notions of "units" in my course and instead weave big ideas throughout my entire course. Instead of teaching a big idea in September, and then only discuss it again during our "final exam review", I would ensure big ideas spanned the entire length of the course.

What are things, thinking back, did you NOT do?