Marveling At The Historical

Math Oldies But Goodies

  • About This Blog

    This blog is mostly about math procedures in textbooks dated from about 1825-1900. I’m writing about them because some of the procedures are exquisite and much more powerful, and simpler, than some of the procedures in current text books. Really!

    I update this blog as frequently as possible ... every 2-3 days. And, if you are a lover of old texts and unique procedures, you might want to talk to me about them, at I’m not an antiquarian; the books I have are dusty, musty, brown-paged scribbled-in texts written by authors with insights into how math works. Unfortunately, most of their procedures have vanished. They’ve been overcome by more traditional perspectives, but you have to realize that at that time, they were teaching the traditional methods.

Math Was … Math Is

Posted by mark schwartz on April 20, 2016


This piece comes from teaching remedial/development math teaching for a lot of years in urban centers and community colleges. I learned to listen to the students and finally gave them an opportunity to talk back, but anonymously. It summarizes and validated what I felt was happening.

The Story; Some Student Thoughts

It would be nice if in most cases, I could take someone with minimal math skills and make them comfortably competent with basic skills, all of this in one term. This doesn’t happen regularly with people with 10-12 years of marginal or negative math experiences. They bring with them fragmented knowledge and also beliefs that math is only for smart people. They simply believe they can’t do it and have had this belief reinforced by teachers and fellow students.

I don’t believe in the concept of “edutainment”, that education must also be entertaining in order to be effective. “Edutainment” focuses on an external condition that the person may respond to but it’s not as valuable, at least in my estimation, as the internal state of a sense of awareness, control, understanding, and mastery from having had a positive math experience. There can be too much entertainment and not enough learning. Of course, math education also can be entertaining, resulting in a sense of accomplishment and joy.

This sense is one we might usually notice in students who have managed to “get it”. Their level of classroom participation increases, they hang around after class to discuss things, they sometimes even arrive early to review something; they attach themselves to you in a mathematical way and they take every opportunity to show you, with pride, that they have somehow permanently crossed that barrier from “don’t get it” to “get it.”

These are nice rewards for an instructor, particularly when by definition you know that the students coming into the class at the beginning of the term are likely to have low performance as well as low opinions of math and themselves as mathematizers.

The obvious goal is to improve the skills but I rarely see a significant shift in skills without a corresponding shift in attitude or affective state. It doesn’t always occur but the likelihood is that if you see a student’s performance improve, you will also see a shift in their identifying math as more approachable and their identifying themselves as more comfortable with math.

I thought I’d ask for some feedback from students on this idea about a shift in cognition having a corresponding shift in affect. I don’t believe I’m alone in sensing this is true or having personal stories to tell. I’m not searching for statistically significant findings; rather I’m looking for what used to be called “just noticeable differences.”

I thought about it and constructed a very simple instrument, asking students near the end of the term to reply to a few questions. It looks like this.

“Please thoughtfully complete the following statements. NAME NOT REQUESTED.”

“When I started math this term I believed math was … “

(down about 1/2 page): “Now that I’m near the end of the term, math is … “

Although I don’t ask for names, there are some students who identify themselves. They typically report a positive shift in affect and are clearly making a statement that they want me to know that they’ve had a good experience. A quick look at their performance (those who provide a name) shows a link between increased affect and increased skills. But that’s not the real point I want to share.

The following are, I believe, a representative sample of responses.

  •  Math was … Evil.   Math is … Evil.
  •  Math was … A bunch of numbers with different values that equal different amounts. It was also not the most fun or interesting thing to do.          Math is … Something I am learning to have fun with and not only seeing as numbers, but as something that can be useful for many other areas of my life.
  •  Math was … Boring and not that important. I had not taken a math class in a few years, because of lack of interest, and a prior experience with a bad teacher. Math is … A lot of fun and interesting. This class has renewed an interest with the science of number relationships.
  •  Math was … A course I would struggle through and pray for a “C”. I suffer from major Math anxiety. Math is … Something I can comprehend and get a better than “C” grade. I’ve gained confidence in my abilities and move on to the next math course.
  •  Math was … Complicated but needed. I also believe that even though I was going to try my hardest I was going to fail. Math is … Still needed but actually … fun! Now I know I was wrong and I’m passing greatly.
  •  Math was … Hard and frustrating. I never enjoyed math and happy when I got a “C” on a test. Math is … Able to be done. This is the 1st time in a while I have done well even though it’s basic stuff. I have a bit of confidence back.
  •  Math was … Something I didn’t remember. It had been a long time since I had used it. I was afraid I couldn’t get fractions and percents. Math is … I am proud of what I know and remember. I can do problems I didn’t think I could. I have actually had fun with this!
  •  Math was … Something that you have, rather than something that you learn and do. The lucky gene club gave math to others not me while I got creativity among other things. Math was impossible, my last fear to face, a constant dread, a source of insecurity – an enemy. Math is … A tamable monster – my toy.
  •  Math was … Easy. Math is … Easy.

I intentionally put the “bookends” of “evil” and “easy” because for some students, this clearly is the case. But, I suspect that as you read these you probably see and hear some of your own students. I’m beginning to have a library of statements that, although anecdotal, are direct expressions identifying that students can overcome an aggregation of bad experiences. For the first respondent, I can only surmise that it has yet to happen since I am an eternal optimist about students not only having the capability but also the spirit to want to know and enjoy themselves as performers in math.

As critical as the shift from negative to positive affect, is the verification of how people feel when they arrive in the class. The general sense of unease is clear at the beginning. But equally as clear is the sense of relief after having had a good experience. The word “fun” appears more than one might expect. Again, I don’t teach the class as entertainment, but when someone is having fun there typically is a sense of ease, comfort, and perhaps exhilaration. I’m going to continue with this little project and at some later date do more reflection on the students’ comments.

These student comments are self explanatory. Some might contend that they are self evident, that of course students with negative experiences and then a positive experience would say such things. But as self evident as they may be, a record of them is I believe, important not for my or your purposes but because of what might be called the “experimenter effect”. I believe that giving an opportunity to students to tell things anonymously that they might otherwise be too shy or ashamed to express is valuable. As several students later commented, they felt that my asking for their beliefs was more important than the beliefs they expressed. The best summary I can give so far was provided by one of the students who simply said “How can I learn math if no one cares if I believe I can?”


2 Responses to “Math Was … Math Is”

  1. sarablack said

    More teachers should ask students about their relationship to math!

  2. sarablack said

    Reblogged this on Sarablack's Blog.

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