6. Stupid, irrelevant pictures. It does not make math more interesting to put a picture of a snowboarder next to a math problem! It actually makes the math problem look less interesting. I love math, but snowboarding usually comes out the winner in that comparison. So take the picture out!

5. Large blocks of text in explanatory or introductory section. If it is more than 3 sentences, most kids won't read it. Why not break up the text? Here's some problems, here's some explanation; alternate through the section.

4. The definitions and statement of ideas tend to be overly complex. Do kids first learning a theorem need its most technical, most correct statement? Or would the gist of it do for a while, with a promise to return to a more precise statement after practicing for a while?

3. Their homework sets never actually save the teacher time. True fact: writing your own problems takes only slightly longer than doing the textbook problems you assign your students. So why not write your own problems, and know exactly what a problem is about?

2. Standalone units. Textbook publishers want their book to be sold in school districts all across the country, so an Algebra 2 textbook will contain lots of topics, many of which an individual district or school might ignore. Texas schools cover X but not Y; California schools cover Y but not X. That means each unit has to be its own thing, isolated from the rest of the topics. Imagine a U.S. history textbook written this way! The ideas are not connected. There is little mixed review. The easiest ideas are not clumped together at the beginning of the year.

1. Not enough problem-solving!

Teachers, it is possible to do better. You can write your own problem sets! Little by little, you can move away from the textbook.

A couple quick pointers:

- GeoGebra is free and awesome for making graphs of functions or geometry diagrams. "Export to clipboard" cuts and pastes seamlessly into Word.

- Start with a section or unit where you think the homework in the book is the weakest. If you can write one problem set per week, you can ditch the textbook in 5 years. If you are on a team, then by pooling resources, you could halve or quarter that time.

- CK-12 has free textbooks, so borrow their problems to pad your own problem sets!

On a related note, Dan Meyer makes some interesting points about the state of digital textbooks. Basically, not enough useful collaborative features to justify them. Here's his full list of suggested features:

Digital devices should allow you to:

- Pose more interesting problems using more diverse media types and fewer words. (eg. three-act-style tasks).

- Replace your textbooks' corny illustrations of mathematical contexts with illustrations from their own lives. Students: find a trapezoid from your own life. Take a photo. Tap upload. Now it's in your textbook.

- Progressively disclose tasks over multiple screens so students don't have to look at pages full of questions and information like this [pdf] and can instead start with a brief video and single sentence.

Networked devices should allow you to:

- See all your friends' illustrations from their own lives. The teacher should be able to see that gallery of trapezoids, promote certain illustrations, and offer comments on others that are visible to everybody.

- Start lessons with integrated, formative polling. I'm talking about Riley Lark's ActivePrompt software built right into the textbook.

- Create student conversations. Use student data to find students who disagree with each other, pair them up, and have them work out their differences. All of that should happen without the teacher having to facilitate it because the device is smart.

- Combine student data for better, more accurate modeling. (eg.Pennies, where each student collects a few data points which are then instantly collected into a much larger class data set.)

I especially agree with the point about more diverse media types (interactive GeoGebra file, anyone?) and disclosing tasks over multiple screens.

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