Slow going for exponential and quadratic functions units

The latest on these two units is that they are in the process of a re-write. As I taught the lessons for each I had too many examples, processes and just good stuff come up that wasn't included in the original investigations. Some shuffling needed to be done to accommodate these new ideas... so I'm hesitant to post the changes yet. I really want to take a good second look at them before they go live.

Keep posted. I am still looking at the end of Febuary for a complete first draft to be complete of the whole alg 1 textbook.

exponential functions links

Here are two great links that can be used withe unit on exponential functions:

This link takes a look at several common fractels and what happens as the number of iterations increases

http://illuminations.nctm.org/ActivityDetail.aspx?ID=17

This link involves paper folding and has some impressive (not intuitive) results:
http://raju.varghese.org/articles/powers2.html

Math and Haiku

http://www.haikulearning.com/ is really teacher friendly website creator specifically designed for teachers.

Check out a friends site at http://www.myhaikuclass.com/kcmowrey/mowreysclass/cms_page/view/30636

It's free too... always a bonus.

Nice twist on charitable contrabutions

Recently on a math teacher forum someone posted an interesting link for teachers: www.donorschoose.org

On this site teachers bid for donations to specific projects... for example, since many of the investigations written assuming the use of the ti-83/84 graphing calculator. But what if you don't have a classroom set? At donorschoose.org it is completely reasonable to finance 8 calcualtors with contrabutions.

True this is not a classroom set, but I could be one calculator for a group of four (assuming a class of less than 32)... then next year you could get 8 more and so on... in four years you could have a classroom set.

Not an ideal solution, but defiantly plausible.

Using the K.I.S.S philosophy in creating an open source textbook

When I was in high school I signed up for auto shop the spring semester of my Junior year. I really wasn't fired up about it, but I needed something in my schedule and it fit. To my absolute supprise, auto shop with Mr. Taylor turned into one of my most favorite classes of all time! I didn't know anything about cars, but I enjoyed puzzles and solving problems. Mr. Tayor was a no-nonsence, tell-it-like-it-is, practical problem solver who taught me the value of the K.I.S.S. philosophy... Keep It Simple Stupid!

Many of the puzzles and problems that we come across, if they are unfamiliar, we tend to try to over complicate. It's one of those things where, when we know the answer, it seems simple and obvious... but when we don't we develop anxiety within ourselves and thus over complicate the matter.

Take the rubics cube for example. When we first grab that thing, it seems darn near impossible to solve. However, we know that there must be a simple answer because there are people who can solve it in less that 30 seconds!

Mr. Taylor taught me to be practice and keep my solution schemes simple. Some would call this Occam's Razor (the simplest answer tends to be the correct answer), but I prefer Mr. Taylor's KISS (because it makes me smile:)

This is the basic philosophy behind the construction of an open source textbook. The basic idea is to develop content to create viable math textbooks using already existing technology. Certainly fancy graphics would be nice, but cant we just draw what we need and use a scanner to put it into a document? Can't we just use the screen capture feature of the graphing calculator to build the graphics we need? Latex equation editors are open source, very high quality and easy to use in google docs... so why not use them?

The point is that at this point developing a coherent content is more important than displaying computer wizardry... there is certainly enough of that on the internet already. As the community of Open Source grows, perhaps there will be more people to develop things like impressive graphic and interactive applets. But for now... K.I.S.S. does the job. Let the text book companies worry about "keeping up with the Jones'" and spend all their money on half hearted graphics that catch the eye of a potential buyer or endless/empty web resources that are made to impress buyers with volume, not quality.

Mr. Taylor would have encouraged me to look to the cause of the problem. Since textbook companies sell their material to a national audience, they are not really interested in meeting the all needs of local educators... rather to create a product that meets (or appears to meet) as many of the needs in as many places as they can to maximize profit.

An open source textbook may not be flashy, yet. But as the community develops it has the potential of creating an editable resource that has a vast list of contributing authors and multiple versions to choose from... absolutely free!

Imagine if every math teacher could look at their classes at the beginning of the semester and tell them, honestly, that they are the author of the textbook that will be used in class.

How cool would that be?

Unit 2 (first draft) is up!

After a few slight changes, unit 2 (two variable equations) is now up on michiganmath.org

The teaching of the material went well... in particular, the investigations at the end of the unit in regards to correlation, lsrl and causation was well received by students.

Coming soon... unit 3... Systems of Linear Equations.

welcome google docs

In search of a good open source solution to my file compatibility woes, I finally settled on google documents. My .docx files created on my windows machine had a hard time opening in mac. When I converted all of the files to the older .doc files, I lost much of the equations converting and much of the formating of the original documents. Plus, it was going to be really hard to keep up with edits and uploads to the mighiganmath.org website.

Google docs seems like a good solution.

Pros:

1. all documents will open in multiple platforms.
2. No longer to upload new files every time there is a revision... I can just make the revision in google and the link on the website works instantly with the new version.
3. Equation editor saves space by using html. Although it is more basic than all the options ms word has to offer, it is more than enough for an algebra 1 or 2 book.
4. I can open the document at times for external editing if I choose.

Cons:

1. documents can only be no more than 2MB with images... 500k of text. (this may be a hidden pro because it will force the documents to be succinct and more easily accomplished in one class period)
2. I have had formating issues when i have exported google docs to ms word in the past. Things get shuffled around.
3. I'm a control freak and the google docs are not in my control... Ie what if something happens to google docs and all of my files are lost, misplaced, corrupted, etc... Of course they will be backed up, but see con #2 for my concern there.

Overall, it is the best of my choices. Microsoft and apple cant seem to make a word that talks to each other smoothly in both platforms (is suspect that this is some type of super corporate wars for market share profits... or something like that). So my open source options LaTex, a wiki or google docs. LaTex is much more powerful and solves the compatibility issue, but requires editor to know a difficult markup language (making it impossible to be edited by non-computer oriented people). Also LaTex doesn't solve the online editing option. A wiki would solve the online editing problem, but for use in the classroom, many teachers will want to print out the investigations and make copies for the class. In my experience, the formating of wikis doesnt always turn out the way you want it when you print. Plus, there is the hassle of finding a "free" wiki that allows for member access by login. Google documents doesn't have this either, but at least I can control "when" the document can be edited.

So google docs it is... for now....

Unit 1 back up!

I finally figured out how I can use my MAC to build the website and properly upload my Office Documents. Anyways, Unit 1 in the draft format is finally up... sorry it took so long.

Do your students a favor… let them struggle!

One of the things great teachers do regularly is monitor their wait time after we ask a question. “Restrain yourself by counting silently for 15 seconds before succumbing to the urge to tell them the correct answer to the question”, was the discussion I had with a colleague recently.

We all want our students to do well, so it is understandable why we want to make sure that the correct answer is out there so that students don’t form misconceptions. But, by not giving students a chance to answer we unintentionally thwart our primary goal… teaching kids how to think mathematically.

Perhaps we should extend this philosophy to every aspect of our classroom. A recent study out of Rutgers University’s Newark Urban Education Department supports this seemingly contradictive statement: “You can raise your school’s test scores by letting them struggle (even get a little frustrated) in algebra class.” (see:http://www.edutopia.org/math-underachieving-mathnext-rutgers-newark)

This article states that, "Most of the literature describes student engagement and motivation as having to do with their attitudes about math -- whether they like it or not," Schorr says. "That's different from the engagement we've found. When students are working on conceptually complex problems in a supportive environment, they do better. They report feeling frustrated, but also satisfaction, pride and a willingness to work harder next time."

And, “Since 2003, the average standardized math test scores among fourth graders in Newark schools have risen from 45 percent to 79 percent.”

As the Michigan Math Opensource textbook develops, on of our focuses is to consider the broader implications of the “wait time” concept. Ask yourself, “Am I the sage on the stage or the guide on the side?” If you find yourself being the sage on the stage a disproportionate amount of the time, you may want to consider adjusting your instructional strategies… and as you begin to use this opensource text you will find plenty of opportunity to be a guide on the side.

are they moving the standards on us again?

Here it comes... hold on to your graduation caps... moving targets in the form of academic standards! This month's flavor... Algebra II. Check out this article presented last summer to michigan principals and consider it a warning shot across our bow (http://mymassp.com/content/michigan_algebra_ii_expectations).

This is exactly why an open source algebra 2 textbook would be highly useful. A flexible/editable textbook can more quickly adapt to changes in curriculum than a static textbook series.

problem with uploads

Well, I thought we were up and running... however, apparently since all of my files were written in microsoft word and labeled .docx, my new mac (bought specifically for this project) wont recognize the files. So every time a mac tries to open the files, even with office for mac... it looks like you are getting messages from the mothership!

Keep posted, I think if I convert all of the files to office 2004... then the files should be able to open on more formats.

Chapter 1 complete

Chapter one is complete and can be downloaded on www.michiganmath.org!

One thing that is very noticeable about the chapter is it's immediate usage of the TI-83 graphing calculator. Since I am able to put a graphing calculator in every one of my students hands, this was not a problem for the field test class. However, what would I do if I didn't have the calculators? Actually... I would simply alter the investigations to take out the graphing calculator parts or combine them into an appendix available for those students who have calculators.

That's really the point of an open source textbook... Everything is written and downloaded in easily edited .doc files. If something doesn't fit, change it. You don't have to subscribe to some textbook publisher's desire to create a national product. That is, textbooks are written to a national audience, but standards and expectations vary slightly from state to state. Only use what you like. Experiment. Customize. Have you ever heard of a textbook that can do that?!! Probably not. Rather, you bought a textbook and said, "I dont like that chapter." or you found mistakes that you couldn't fix because you couldn't access the text.

So for me, the graphing calculator section early and throughout the text works... but it if it doesn't for you, change it. You'll find the changes are most likely minor because the basic structure is already there.

www.mathtv.com ... great resource for OpenSource text

If you haven't had the opportunity yet, visit www.mathtv.com. To see the videos you have to subscribe, but don't panic... it is free to subscribe! And if you are worried about getting a lot of junk email newsletters crowding up your inbox, just don't choose the newsletter box (with is not checked by default).

The videos are of high quality and are put together by professional educators. The authors of the site do a great job at problem selection and presentation. On most of the videos, you (or your students) can pick which presenter you would like. On many (but not all) of the topics, there includes a presentation in spanish as well. I really love this feature! I find myself watching the spanish presenters more than the english presenters. Since I already know the math and mathematics itself is universal, I find it refreshing to hear it in spanish.

If you have ever been part of a selection committee of a new textbook, you will have noticed that the major textbook companies try to entice you with features like the videos presented on MathTV. But that is the nice thing about the open source movement, most of these features that are advertised are already available in the online community... if you know where to look.

Speaking of advertizing, this is the one slightly annoying feature of MathTV... commercials. As you click from video to video, commercials will come up during the transition. You dont have to watch them and they will end as soon as you start your next video. Now only if my TV at home would do this! Maybe MathTiVo would have been a better name for this site:)

In later posts we will explore how to opensource the worksheet generators that textbook companies package in their products... stay tuned!

First week investigations - real number systems

I teach in an 85 minute 4x4 block schedule. This means that I have approximately 90 days of instruction that I can use to teach a course in algebra 1. Personally, I really like this schedule for teaching math and science.

For example, this week was a 3 day week due to labor day was Monday and Tuesday was the first day of school... so my class did housekeeping stuff like review of the syllabus, getting textbooks, getting to know you activities, and (because we had time) I introduced the real numbers using a venn diagram... then I had the students make attractive posters of that could be posted in the room. Many of them were really good, so I posted in the room and gave those students an extra credit point. What a great way to start the year!

Other than that I taught two investigations: U1A1- Natural Numbers, Whole Numbers and Integers and U1A2- Rational and Irrational Numbers investigation. The natural numbers investigation is posted on the michiganmath.org website, but the site is still largely under construction... but if you want to download it, then you can.

I spent one day on U1A1 and two days on U1A2. Day one was fantastic! I really felt like I accomplished my goal of properly introducing students our brand of "mathematical" critical thinking. I introduced the topic with a "what do you Know, what do you Want to know and what have you Learned"... or KWL strategy. Next I went over the text portion of investigation with the students.

It is important not to spend too much time lecturing... our goal should to become the "guide on the side" rather than the "sage on the stage". For this investigation, no more than 15-20 minutes is necessary. The goal is to provide students with as many "looks" at the material as we can... students need to see it, hear and feel it. So it is important to give them information (and you can use a variety of strategies other than lecture to do this) so they see it modeled properly and hear it modeled properly. But, and this is the really important part of this textbook, you have to give students time to work on the investigation questions in class where you can guide them when they need help... thus, they know how it "feels" to do it properly before they practice independently.

These investigations are designed to such that most students can complete 80% of the material in class and 20% of the material at home. If I taught in a 45 minute hour, I would have stretched this out over two days and followed this 80/20 rule for assigning homework on the first night. Also, don't be afraid to give a "hand-waving" explanations of how to do what you anticipate as "difficult" questions.

For example, in this investigation, it is a good idea to explain to students about the modular arithmetic problems before you assign them the problem. Also, the terminology of natural, whole and integer can get confusing. Consider the problem that talks about fractions being integers or rational numbers... this is another good one to go over before you assign. This being said, however, it is not a good idea to explain all of the problems before they try them... allowing students the gift of figuring it out themselves will mean more to them than depending on you for answers. Our goal as teachers should be to wean them off of us... not make them dependant upon us (or should I say, us being co-dependent).

As for how the investigation went in class, I can say that I am pleased and we had a good start.

The reason I spent two days on U1A2 is due to the amount of longwinded explanation I gave of rational numbers. Apparently, I fell into my own trap! As the author, I can get caught up in every detail of what everything the text says. For example, There is proof of why sqroot of 2 is irrational. And although this is an interesting proof, it can easily be left to the student to read on their own time if they are interested. Again the real value of the investigation is that you teach students something and then you immediately give them an opportunity to use that knowledge and you constantly are providing them feedback.

In retrospect, I could have done this investigation in one day if i split the class into 45 minutes of introduction and practice with rationals first, then 40 minutes of instruction and practice with irrationals. Other than that, I was again pleased the format of the lesson and the questions students asked about how to do the mathematics. GREAT START... stay tuned.

Hello World...

It only seems appropriate to start this blog with the phrase "hello world..." Traditionally, this is the first thing a programmer learns to do when they are learning a new language. So I will make it the title of my first post. This title acknowledges a paradigm shift from traditional (static) textbook to an open source collaborative (dynamic) textbook... so... hello world... Hello World.... HELLO WORLD... this is the open source movement, its coming to educators and it's here to stay!

Last summer (2009), I developed a collection of math "investigations" that are organized around standard set fourth by the State of Michigan (High School Content Expectations... or... HSCE's). Although there is a complete list of expectations for grades 9-12, this first online textbook will focus on solely on Algebra I content. With an emphasis on a "functions approach" to algebra, the basic philosophy of the text will be to develop a course that is rigorous, relevant and relationship oriented. For a complete list of these standards you can visit the Michigan Department of Education at http://www.michigan.gov/mde/0,1607,7-140-38924_41644_42668---,00.html or you can find it a www.michiganmath.org when the website is up and running.

These investigations are a culmination of my experiences over 15 years of math teaching experience... But the point this experiment is not to create a static non-reactive text, but to incorporate others experiences and knowledge to add to the collective work and greater good. Consider these initial investigations as the "base" of a soup.... but the soup wont be truly delicious until we add all of the bit of carats, celery, and spices that make a "miraculous" soup.

But no amount of "grand analogy" or "resume boasting" will change the fact that as of yet... these investigations are untested. When www.michiganmath.org is finally constructed the textbook will be online, but many investigations will have the marker "DRAFT" next to it until each as at least been field tested once. Sometimes an idea that sounds great in July looks ridiculous in November! I will try to keep readers up to date on changes in content and delivery, basic pedagogy/philosophy of project and updates on implementation pros and cons...

This textbook (as a draft or not) will be available, free of charge, to anyone who would like to use it or alter it to fit their needs in the classroom, school, district, county or state. All the material is presented in a word document and easily altered and printed to meet your specific needs.

So off we go... hold on to your hats:)