Learner Activities

What makes a great activity? Certainly one that is engaging and motivating. Chapter 5 discusses two types of learning approaches: direct instruction and inquiry-based learning. Activities can be either. Basically "direct instruction" activities are where it is clear what skills need to be acquired and it is clearly layed out how to acquire them. The focus is on gaining proficiency not quelching curiosity. Inquiry-based is where the ends aren't quite clear; where you need to be curious and find out what type of answer you need before even finding it. For instance, if the topic is slope-intercept, a direct instruction activity focuses on teaching what slope and the y-intercept are. It states the facts, then works on the skills necessary for proficiency. An inquiry-based approach is if a student comes to an understanding through exploration-- like looking at real life examples of a changing rate; like phone rate plans for example.
Obviously the latter seems more engaging, however, procedural proficiency is definitely necessary. It is difficult to differentiate procedures in math, but topics can be explained in a variety of ways, and at a slower pace, for those learners who need more processing time. The more interactive, curiousity-sparking activities are more easily differentiate-able, especially with on-line actitivites, where for instance you can't move on to the next level until you've demonstrated enough proficiency. The activity grows in complexity as the student gets better at their own pace.

The topic for my curriculum web is slope and y-intercept. These websites I found to be helpful. I put them in order of when they would come into play in instruction. The first offers an introduction, the second is for the learning, and the third is for the assessment. The level of interactivity goes from least to most.

http://www.math-play.com/Slope-Intercept/Slope_Intercept.html
This one might be a little boring- not a game-, but it is interactive and a helpful introduction to this topic. It allows students to change the slope and the y-intercept and see the resulting line. It also asks probing questions for the students to start thinking about the consequences of changing the slope and the y-intercept.

http://www.mathwarehouse.com/algebra/linear_equation/slope-intercept-form.php
This website is nice because the students can use it at home to help them self-teach, or it can be used in class. It has boxes to click on for the answer. Therefore, you could put the site up on a smart board, and give the class time to work out the problems, then click on the automated response. It also has the sliding line, so students can control slope and y-intercept, and not only see the line created, but also a table of values.

http://hotmath.com/hotmath_help/games/kp/Karappan_Poochi_Sound.swf
O wow! This site is AMAZING! It is a fun game for kids. Basically, cockroaches crawl across the screen in a straight line. There are three rounds- first is the easiest, find the y-intercept; second, find the slope; and third, find the equation of the line the cockroaches crawl on. Once you type it in, a laser shoots them and they die. It is timed, so after a few minutes, you lose that turn and have to try again. You need to reach a certain proficiency to be able to move on. It is challenging and fun!!!! So easy for differentiation- since you move on as you get better.

Curriculum Area- relation to technology

While technology can probably be used to aid in teaching any subject, it is most readily apparent that this is the case in teaching math and science. As a math teacher, I have found several ways that I utilize technology in my classroom: calculators, the projector, and the smart board. I am really only comfortable using the first two of these. But oddly, I have found that even my 8th graders are unfamiliar with using calculators and often don't type in the appropriate order. I did not push this, which I probably should have, since most of the state exam cannot be completed with a calculator, and my students' basic computation skills are severely lacking. In hindsight I really ought to have used the calculators more in my classroom, especially since for the extended response section, where they can use them, they are rather clueless. I did just receive a large overhead calculator aid, so I think this will help me teach my kids how to use one. It's probably too late this year. Yikes! As for the projector, I have actually just received one and am getting accustomed to using it. It is slightly awkward to write on, but I think my students appreciated the change of pace. It is really useful for the overhead algebra tiles! I finally got my internet connection for my classroom and really should learn how to use the smart board. It is so intimidating, however, and I am not sure I am ready for it. Maybe once I make some curriculum webs of my own, my eagerness to share those will override my hesitancy of using the smart board.
Technology is especially useful in teaching math, both because it sparks interest in what can be a rather dry subject, and because it makes rather abstract concepts more readily apparent . The internet and education websites provide great animations and other aids to explain difficult topics. But more than that, technology is the way to bridge the gap between the classroom and the real world. Mathematicians today rely on technology. And computers, which most certainly fascinate our kids, rely on math. Technology can help us help our students to not only understand the math we're teaching, but also to inspire a curiosity into how math affects the world around them.

Website Evaluation

There are five main questions to ask yourself when trying to evaluate a website: the five w's : who, what, where, when, why (created by Kathy Schrock-- I'm practicing upholding copyright laws!) These questions are very good to ask yourself because not all websites are equally useful. Some may have incorrect information on them; may falsely claim to be unbiased; may represent the information in a confusing way. Especially if you want to use technology and websites in your classroom instruction, you don't want to be infront of the students googling "polynomials" for the first time and then just randomly clicking on links (unless random searching is what you're teaching, of course). You will want to know ahead of time which websites are useful, accessible, and represent the information both accurately and clearly. I really did not have any idea how many useless/less valuable websites there are for math. Useless because they are targeted for high school or college level students. Nowadays it is almost always better to get an interactive, animated website rather than just dry, typed up notes/walk-through of procedures. Another reason you want to check out websites for evaluation before telling links to students is that many for education are not free!? So much on the internet is free, but many organizations put together a huge database for teachers but you need to pay for subscriptions. Also- if you have a wireless network at your school and want to show sites, many are restricted as soon as you get to school because of the board of education's restrictions. This is why it was useful in class when we were talking about education-y alternatives to you-tube (on which at home you can view really helpful, awesome animations of a variety of math topics).

Very Helpful Math Websites

Many uses for Algebra Tiles:
http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles.htm


For a variety of interactive manipulative-friendly lessons:
http://nlvm.usu.edu/en/NAV/topic_t_3.html

The Impact of Copyright on Educators

The chapter that we had to read for last week's class discusses copyright regulations and a loop hole for teachers called "Fair Use." Basically something can be copied if it is a small portion of the whole; if it would be, time-wise, impossible to seek permission, and if the copy is for only one class and one course. It is mentioned that all copies should be returned to the teacher before students leave the room with them; that the teacher should only keep one copy for herself. What is most pertinent to me was the sentence that talks about how copying pages from a workbook is not ok.
I understand that copyright was put into place to give rights to the authors of works. I can completely understand not being able to say copy an entire book and distribute that. But math workbooks?! I do not feel like photocopying workbooks destroys the integrity of the work in any way. The issue of copyrighting as presented in this course's textbook conflates "illegal" and "unethical." These are not necessarily the same thing (murder, for instance, is obviously both- speeding is certainly not unethical). It is completely unrealistic as well, since while the schools usually provide each student with some type of workbook, teachers typically run across another source that they want their students to work through. As with many things I think it is more important to follow the spirit of the law rather than the letter of the law. But clearly the number of court cases and monetary settlements reached because of copyright infringement is evidence that this is not how the law works.