Response to Educational Blogs

I was happy to look again at Deb's Math Blog today.  It was great timing because there were some quick little quizzes on finding the line of symmetry in a quadratic function.  There were also some great PDF worksheets on solving quadratic functions by factoring, completing the square, and using the quadratic formula.  The timing was great because I am beginning the chapter on all of these topics this week with my Honors Algebra 1 class.  Our Prentice Hall textbook is a little bit on the easy side, so I am always looking for some challenging problems for my honors class.

There was also an interesting post about the relationship between exercise and math.  Apparently a new study came out saying that people are better able to solve mathematical problems if they exercise.  This makes sense to me.  I guess this is motivation to exercise more!

Lastly, I saw a cool post on Maria Andersen's Blog.  She teaches math at a community college.  She posted a video to show how she completely changed the atmosphere of her classroom.  She got rid of all of the forward facing desks, and replace them with large tables.  Her students spend a good percentage of their time together at the white boards working out problems in groups or pairs.  This is great because it makes the class more fun, and the students are learning more.

My website

Check out my website.  It is a work in progress.

http://sites.google.com/site/mauraswebsite

Inquiry-based Learning

It seems to me that the only appropriate way to teach math is through inquiry-based learning.  I've definitely heard of the term, but never really knew what it meant.  I did assume that it had something to do with asking questions.  As a math teacher, I use inquiry-based learning.  For example, I might model how to solve a math problem to my class.  I might start out the problem, but I always have my students help to solve the problem.  Sometimes one student will solve the whole problem, and other times I might have a few different students involved in performing the steps.  The first problem that I model is typically easier.  I always make sure to give my students different types of problems that will provoke different questions.  Typically, each problem will have a new level of difficulty.

When students ask me a question about how to solve a problem, I often respond, "I don't know, you tell me".  When the student is forced to try this on his own (maybe with some helpful hints), he is more likely to retain the information.  Obviously, most students will not remember all of the specifics in Mathematics, but it is my job as a math teacher to help my students to become good problem solvers in their personal and professional lives.

Also, a quick word about historical thinking.  As a high school student, I never liked history.  I remember social studies as just being a series of dates, treaties, wars, etc. that I had to memorize.  As an adult, I think that studying history is extremely interesting.  Recently, my daughter told me that she loves her high school history class.  Her teacher makes history seem so interesting and exciting.  She tells her students to just think of history as one big soap opera - people (or nations) fall in love, they fight, then they break up.  This is the way to learn about history.  It brings all of the people and events to life!

UDL Concept Map

UDL is important because it offers students more options for learning.  In particular, UDL is geared to benefit students with different learning styles, different backgrounds or cultures, different abilities, or disabilities.  The three basic principles of UDL are to support strategic, recognition and affective learning by providing students with more learning options.  UDL allows for more access to learning as opposed to access to information.  This gives the student more resistance and challenge and therefore helps the student to learn how to learn.  UDL allows us to rethink how we teach.  By setting clear goals, providing instruction to obtain these goals, and continuing to assess progress, we, as educators, can provide a better education for our students. 

Graphing parabolas image

I created this image because it will be useful for my Algebra 1 class.  I will show this image to my students at the beginning of the chapter on graphing quadratic functions.  I think that my students will enjoy this because the boy in the image is one of their freshman classmates (he's also my son). 

I will ask the boys to focus on the actual parabola.  I will ask first what they notice about it.  What is the shape of it - is it opening upward or downward?  Where does it intercept the y-axis?  How many times does it intercept the y-axis?  Where does it intercept the x-axis?  How many times does it intercept the x-axis?  Does it have a highest or lowest point, and if so, what is it?  Is it symmetric?  What does the equation for this parabola look like?

Toward the end of the chapter, when the students have learned how to graph quadratics, I will show the image again.  Hopefully, this time they will be able to give more information about the quadratic equation.