Memorial Day

A week before the Summer Session starts and we remember the many who gave their lives for our freedom. As I think about those who died in war I started thinking about those whom our country has fought against. One of the greatest enemies was, I think we can all agree, Hitler and Nazi Germany.

There is a reason that I think of this.

Hitler and the Nazis were anti-intellectuals. If it did not serve their narrow world view, or their militaristic needs, they were opposed to it. Also, because of the ideology of Aryan superiority, they drove out all Jews, and others that they considered 'alien' from their universities. Many who were not Jewish left because they felt threatened by the rising tide of Nazism.

Whenever there are those that cry out against scientists and mathematicians I cringe. May we never again see anti-intellectualism rise to such a level again.

Here are some links to further investigate the effect that Nazism had on the academy in Germany.


Review of a book about Mathematicians fleeing Nazi Germany.

Nazis and Mathematics (online book)

Nazi Education

Mathematics in Nazi Germany

Power to the Students!

Most of this last week has been spent on technical issues, like how to record lectures to upload so that I can implement the flipped classroom.  Not exactly the type of thing that anyone wants to read about, kind of like learning how sausages are made. So I am left wondering what I can write about that more about the what of teaching as opposed to the how that I have been mired in.

As I was looking at the text for the summer I got my inspiration,

                                          EXPONENTS!

Teaching the rules of integer exponents in most texts drives me crazy. This was one of the places where, as a student, I was left feeling like it was magic. Or, as one of my mentors when I was an undergrad put it, like a bunch of mathematicians got together, got drunk, and decided it. Of course, that’s not the case, but how do we convey that to our students?

After introducing how to work integer exponents, what most texts (including the one I am using this summer) do is go straight to the “because” of a⁰ = 1.

What witchcraft is this?

A lot of texts will immediately follow that with a^-n = 1/aⁿ.

And by this point, if you ask students why the only response I have ever gotten is ,”Because that’s what they taught us.”

                                                              NO! NO! NO!

If we are really intending to teach our students mathematical thinking, then we need to pull back the curtain and teach them how we use the definition of exponents to build all of the rules we give them. Just like in Geometry where we start with postulates and build all of Plane Geometry, we build Algebra, and all mathematics, the same way. If we follow the original definition(s) where does that take us?

So, how can we do this with exponents?

Here is part of the worksheet that I will be giving to my students. This is how I used to do my lecture, and while I will do part of this in my videotaped lecture, I want to leave as much as I can for them to discover on their own.

This is known Experiential Learning. It is not surprising that research has shown that students have greater retention when involved in Experiential Learning than they do when taught in a regular lecture setting. I have talked in prior posts about the different needs of adult students, and this is one way to get them actively involved.

As always, feedback is welcome.

Bumps in the road

As I am preparing for the Summer Session, it has started to dawn on me that I had not really considered how much effort is involved in changing from a largely traditional mode of teaching to a flipped classroom. And while I am still committed to these changes, I understand better why I have never done this before, and why so few adjunct would take the time to do this. I am going to be putting in many hours of prep-work, none of which will I be compensated for. If I was a full time instructor at least some of the work could be done during my on-campus office hours.

The first obstacle that I have really encountered is preparing some type of lecture material for the students to view outside of class. In order to simplify things the first thing I did was go to the online material provided by the publisher. In reviewing the material provided for the PreAlgebra review was unimpressive. I will tell students it’s available, but I will be surprised if the students use it. So now I need to look at how I can record lectures and make them available to students.

I have connected with the person on campus who does tape and post lectures for professors who do online classes, but he is really busy and I’m not sure how much we will be able to do. He is going to talk to his supervisor and get back in touch with me so we can see what we can get done between now and the start of Summer. I am going to see if I can tape and upload lectures myself. The only trick there will be finding a place, as the main part of the library will be closed for the next three weeks.

The other thing I realized is that I am going to need to prepare the students for what is going to be going on. Since this is not going to be a “normal” class, I should probably warn students before they walk in the door. First thing I am going to do is send everyone an email a week before the semester starts explaining what we are going to be doing. I am also giving them a check list of things to do to make sure they are ready to go on the first day. I am also going to have to completely rewrite my syllabus and redesign how I will be grading students.

One of the things I am also looking at is using problems from Mathematics Teacher for the classroom work, or designing some of my own, so that I don’t become just a different version of the professor who hands out worksheets for students to work on. If I can make at least one interesting project per chapter, I think that will help a lot.

Next week I will have more projects to share.

If you have any classroom projects that you have done for Elementary Algebra (Algebra I) I would be very interested in hearing about them.

Only a month to prep

When I started working on my summer course late last week I found myself struggling with how I am going to implement the innovative techniques that I have been investigating and am enthusiastic about.

I started out as I always do by making the schedule for the whole semester. One basic of teaching a Developmental Math course is that you have some very strict objectives to make sure that students go onto the next class fully prepared. As someone who, especially in the context of math class, wants to know what the rules are, I have always found security in this. However this can also make adapting to students needs a bit tricky at times.

I made sure to include both the review chapter at the beginning of the book and time on the first chapter which is also review. As I started working on the out of class assignments for both of those so that classroom time could be more about student questions I found myself slipping into old patterns and struggling to get out of that trap.

The trap: Online problems, textbook problems, ask for help on those questions. YUCK!

Then a blog post popped up on my Facebook feed with the provocative title “Are we Killing Students Love of Math?” As I was reading this I realized that I need to work harder to get out of the trap. I also realized why it is so easy to fall into that trap. Doing something new and different takes a lot of time.

I love what I teach. I want to share what I teach. But, as an adjunct professor I am lucky if I get paid for office hours to meet with students, and I definitely don’t get paid for prep time. Also, I usually don’t have an office. That means that all of my prep has to come on my own time in a place away from school. I know people who are very disciplined and able to work from home, but I am not one of those people. So this means that I have got to get out of the house and find a place to work. Because of this, it is easier just to assign problems from the book.

But, I also know that once I have come up with material for a course, using it when I teach the course again will not take all that time, so I just need to suck it up and put the work in now. That’s what I’m doing today, and what I am promising myself that I will keep doing as I prepare for the Summer Semester. Sharing what I am doing by blogging is my way of staying accountable, since I don't have my own professor giving me the stink eye if I don't do the work.

I agree with Alice Keeler that doing problem after problem of exactly the same thing can be mind numbing and not particularly helpful. What I do like is the online homework provided by the publisher. It gives students instant feedback, and provides a variety of tools to help them if they are struggling, from walking them through the problem step by step to videotaped lectures. I also limit the number of problems I assign, only 20 per section, so that they are not doing the same type of problems over and over again. I encourage students to do those first, so that they can get a feel for what they are doing and feel confident before they switch to paper and pencil (no pen thank you very much) problems.

So what about the paper and pencil work? I could have them do the same problems from the book just like I and everyone else I know have done forever, but that doesn’t fit with what I am trying to do. So rather than that, I am going to spend my time working on worksheets to do before class to get students to think and come to class with questions. This is part of how to make a flipped classroom which I talked about in my post from March 20th.

I am going to attach examples to this and future posts, and I would love feedback on them. Please remember that everything I post here is covered by a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International License.

For those that are interested I am using the text Introductory Algebra, 12^th Edition. Bittinger, Beecher, Johnson. Pearson. ISBN 0-321-86796-3.

The Prealgebra Review chapter consists of the following sections:

·         Factoring, GCF, LCM

·         Fraction Notation

·         Decimal Notation

·         Percent Notation

·         Exponential Notation and Order of Operations

In looking through the sections I decided that I would have a Pre-Prealgebra sheet on what the different numbers sets are. (Both of the worksheets I reference are here.)

 I like the idea of starting the semester with getting the students to do their own research and writing things out, hopefully in their own words. I do ask them not to copy and paste, but there are always those that try to sneak past the copy and paste, so I am making sure that they cite their sources. This will mean a bit of work for me on their first couple of assignments as I check to see if there is any plagiarism. I often get push back on this when students do projects along the lines of, “But this is a math course not a _____ course.” This gives me an opportunity to talk about the ethics that are important to academics.

I have also finished my sheet for the first review section. I am mixing in textbook problems, but I am working in getting them to think about what they are doing.  (On the sheet for students there is, of course, room for them to answer.)

I do know that for the first day of class most of the students will not have done work ahead of time, but since we are going to be in a classroom with computers it will not be hard to get them going, and by setting that standard at the start it should be easier to get them in track for the rest of the semester. I am planning to email a whole bunch of things to them a week before the semester starts, and since there has been a long break before the summer starts and I hope this will help encourage them to get going on the work.

Any comments or suggestions are always welcome. Have a good week everyone.