I bought a handful of math texts at Half Price Books this weekend. I opened up a Basic Mathematics text and the first thing that caught my eye was the intro titled “To the Student: Success in Mathematics.”

“Really?” thought I. As I read it, I grew more and more agitated.

Have these folks spent any time inside a math classroom? Did they pay attention to the students? If so, they should know that the likelihood of a student to do what they suggested is downright ridiculous. So why do we tell students to do it? Why can’t we give them tips that they *can* and *will* do? Like these:

- If you feel comfortable asking questions in class, do it. If not, write your questions down to ask later. You don’t have to ask the instructor, especially if he or she is intimidating. Find a tutor or go to the school’s math lab instead. You don’t have to work with someone you’re uncomfortable with.
- Read the stuff inside the gray boxes. We know it’s likely you’ll not read the text, but the things inside the gray boxes are really helpful.
- Before you start on your homework assignment, do something physical or something you can do well. Run a mile, do a load of laundry or play tennis for a half hour. This will remind you of the things you are good at and get your endorphins flowing. It will help you be confident during your homework time.
- Absorb the lectures, don’t copy them. If you can do it, try to just watch. See how the teacher thinks through a problem. You will gain more from this than from frantically trying to copy everything.
- If you do take lecture notes, don’t dwell on notes that you can’t figure out. Many times you mis-copy or mis-write things the teacher wrote or said. If it doesn’t make sense, move on.
- Tear out the back of this book (the part with all the answers) and burn it. It is important that you build your confidence. Checking your work with the magical back of the book just gives you a crutch. And don’t use a calculator to “check your work.” That’s just another crutch.
- Do the first two problems in every section and subsection. If you can do those, do the last two. If you can do those too, continue to the next subsection. Math isn’t a spectator sport, but it isn’t an elliptical machine either. Do all the problems if you need the practice. And if you have it down, move on.

Give it a shot. Let the students know that what they want to do is okay to do. Let’s quit giving them the B.S. that’s been passed down to us over the last few decades. It’s time to go Math Book 2.0.

Whatcha think? What’d I miss? Let me know in the comments.

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Love it! I don’t read every post, but what I do read is spot on…looking forward to see what partnerships you create to share your knowledge.

Bon, I really appreciate #1, #2, and #7.

#1: Making a note for later removes anxiety and frustration.

#2: Students process and perform in chunks.. so it makes sense to take in chunks. I personally think textbooks should be delivered in smaller chunks, half the size, and with more visuals that encourage students to think.

#7: Most concepts/problems are listed in sequential order. You noted a savvy strategy that will save time and allow students to decide what’s necessary for him/her individually.

All kids are different, but if we can build their confidence by focusing on what they know, encouraging them to take chances, letting them know that making a mistake is okay, we will have happy kids who want to learn. I teach seniors at a design college and this approach works for them and it has worked for my daughters through grade school and high school.

I like your comment about not taking notes during lectures. I actually request that kids not take notes. I trust that they will absorb what they need to know. And it allows me to see their faces and to know if they are getting what I am saying.

Thanks for you post.

Disagree with 6 completely. They need to build confidence by knowing they are right or knowing where to learn more. The back has answers and not the work. A student still has to figure out how to get the answer. It’s no crutch.

Thanks for your thoughts, Michael.

It’s even worse that the back has no work. If for some reason the back has an error or there are various right answers (only one of which is in the back), a student could be doing perfectly acceptable word and get severely discouraged. I’ve seen it happen many times.

All the 7 points are well pointed out however I can add one more important reminder as per me.

In order to succeed in Math, one has to practice, practice and practice even more to get their basics and knowledge sharpened all the time.

A great article once again by you my cousin, thanks again for leading the way.

Best wishes

Vijay

I like all of your comments except number 6. You suggest that having the answers is a crutch and undermines confidence. I feel that the opposite is true. In fact I often lament the fact that math textbooks only have the answers to the odd-numbered problems. I find that my confidence is built each time I see that the book’s answer matches mine. Also, using a calculator lets me focus on the logic of the solution by freeing me of the tedium of calculation.

But what happens when you’re in the real world? You have to solve problems (and issues) everyday with no “back of the book” to support you. What do you do then?

To me answers in the back are there for the first half of the learning curve. The second half of the learning curve removes the crutches and that is where the deep learning happens.

Unfortunately, the normal sequence is to move straight from practice on textbook problems to the summative crutch-free test. Even with quizzes in between, there will only be one quiz, if that.

Worse, the test is for a grade, not for learning, unless we are in a mastery-based program (the ideal, I think).

No3 is more important than we realise. When my daughters was quite young she would say that she needed a break to ‘run around the garden’ during homework sessions. When we learned times tables we would count in groups and throw a ball between us while calling out the numbers e.g 3, 6, 9, … This kinesthetic approach helped her to keep focussed.

Movement is crazy helpful. Thanks Andrea for sharing your story of this.

I think having the answer is vital – what if 20 questions are done only to find that next class they are all incorrect? I would never set homework or exercise work where there are no answers. Textbooks that have worked solutions as well as the answer, are the best.

If they are all incorrect, then how cool – it means you’ve figured out a consistently incorrect way to do it. So there’s only one thing to fix.

If instead, you find that the back has an error in the solutions, you’ll struggle, always thinking that YOU are wrong. Furthermore, you’ll have no idea how they are doing the problem and how that compares with how you do it.

My suggestion: figure out a different way to do it. So that you can check yourself.

What a nice present for my birthday (last year)! Just yesterday I was thinking about having a button in my app that students could hit when they think they are right and my app is wrong.

We will need a contest to label that button. In football they “Contest (the ruling)”, in court we “Appeal”. My first thought was “Insist”.

My big fear is that students will get addicted to that button. Sometimes we just miss something. It also creates doubt about the software, which I think would be crippling to its worth. Video games do not have buttons we can press to get to the next level when we think a level is unfair.

Perhaps it is better to test, test, test and fix, fix, fix — software can be changed in an hour, paper textbooks — do they send out errata?

Ah, yes, that does sound more like the real world classrooms I knew. All your points have merit, two stand out:

I loved #4 because it confirms my game plan back in the day when I was a student. Just listen! It is great advice to the kids and (“Yes and”!) and I suggest a corollary for the teacher: Don’t *let* them take notes. Not literally, but every chalk talk should be a conversation with the students that keeps them too busy to take notes. Call on a different student for every step or half step, and call on students to correct (or confirm) steps. Gauge carefully on whom you call, using strong students at first until others have seen more examples and gotten up to speed, and always nail the ones starting to daydream. Keeps them alert (am I next? I am if I am not listening, they soon learn.) and it’s more fun for everyone. It was also a bit of a formative group oral exam — if I was not getting the idea across, I knew at once!

#6 ironically holds within a powerful argument for learning Algebra. (Even Ted talks argue against teaching Algebra these days: https://www.youtube.com/watch?v=xyowJZxrtbg). Yes, doing well at one thing puts us in the right mindset for the next, more so if we had to struggle to master the first thing. For many then, Algebra will be the perfect launchpad for all future academic travail. Here is an entire summer program based on that premise: http://svefoundation.org/kids-step-up-to-algebra