Yay for Algebra 2! #MTBoS30 - 11

There's a lot of discussion tonight on Twitter about the merits of Algebra 2 or the lack thereof.

The heart of the question seems to be should it be required for graduation.  In my state, the typical graduation path does require Algebra 2 and it doesn't seem to be keeping students from graduating.  Our graduation rate statewide is about 88% and in our district 97%.

In our high school in particular we are trying to address the statistics that say students are not ready for college math when they arrive, and therefore required to take remedial courses.  One goal for the past two years has been to focus on college/career readiness ... making sure our students have the math they need to take the next steps.  Algebra 2 is an important part of that puzzle.

I'm thinking aloud tonight about the merits of Algebra 2 ...

I think of math as the study of patterns.  In Algebra 2 we focus on patterns in the form of functions.

One huge focus in our program is analyzing the graphs of functions ... understanding key attributes, learning about transformations, using graphs to predict and make decisions.

Yes, the predictions and decision making are often in contrived scenarios, but I think of those like learning to drive in a parking lot before actually getting out on the road.

We also look at real data, determining lines of best fit.  Most recently we explored population, crime, unemployment, and property tax data to see how those in government might use data for decision making.  We also looked at real costs of college tuition in the past 10 years to make predictions about the cost in the next 4 to 8 years.

A second focus in our program is algebraic manipulation - solving equations of all types within the eight functions we study.  There is much satisfaction in solving challenging equations.   Students develop a sense of accomplishment; they are proud of the work they can do.  I borrowed Mr. Waddell's rules about making one or zero ... really helps to clarify the purpose in each step in solving.

The third focus is applying the use of functions to problem solving situations.  Again, the situations are contrived.  Sometimes they are a little bit relevant to students.  Sometimes students seem to be interested in the scenarios.  We use hands-on labs where possible to add engagement.

So why is this course important?

• It wraps up core content associated with algebra
• It sets the stage for advanced algebra/precalculus for students who want to go on with math
• It provides windows of opportunities for students to see how math is used in future job possibilities
• It addresses problem solving, multiple representations, use of technology, and quantitative literacy

A few observations ...

• Algebra 2 content seems to differ quite a bit.  I wonder if narrowing the focus, clarifying the key ideas for the course would help?  I happen to like our curriculum ... and we don't address trig, conics, or probability.  Those topics are attached to our precalculus course.
• Relevance, connections to real world seem to be unclear.  I wonder if MTBoS teachers could crowdsource connections to better problems?
• If it really is "how" we teach and not "what" ... then let's pull together the best examples of what the "how" should look like!

Blogosphere ... Good Ideas!

As I was working on my Feedly list, I visited a number of blogs today.  I am really bad about remembering good ideas that I see around the blogosphere.  So I was delighted when I happened up the radical rational ... where she mentions reading three blogs a day.  She blogged about the three great ideas that she found today ... which sent me on my own hunt for three ideas to use next year!

One of my goals for next year is to do more with math vocabulary.  So I was delighted to find this simple self-reflection on vocabulary at Math = Love!  I remember reading about this strategy in Marzano's book on vocabulary but I didn't put it into practice this past year.  Creating a master list for each unit, rating before, in the middle and at the end of the unit will be helpful in getting students to think about their own understanding of math terms.  (And ... Sarah mentioned a book I might need to add to my summer reading list ... Styles and Strategies for Teaching High School Mathematics: 21 Techniques for Differentiating Instruction and Assessment!

I was not satisfied with my math notebooking efforts this past year.  I value keeping a well-organized notebook but doing so is not one of my skills!  I am afraid that I passed on my lack of organization to my students this past year.  So I was glad to run across Borsht with Anna's post on math notebooking in a 3-ring binder!  Our print shop will copy assignments on hole punched paper. Hole punching is so much easier than gluing and pasting!  I'm hoping that with this plan in place I can teach myself and my ninth graders how to keep each unit organized!

Last but not least, I visited Math Munch today.  Wow!  So many possibilities!  I love the numeric design project.  I had some doodlers this year that would have loved to created graphic design numbers for me!  The Math Munch folks highlighted a TED video presented by Nina Fetterman on epidemics. I can imagine using this video (or a clip of it) as I introduce exponential numbers - talking about the spread of disease!  An ongoing effort is capturing students' attention and interest.  I'm thinking there will be ways to use Math Munch next year ... maybe even "math munch Mondays!"

As you peruse the Internet this summer, how are you organizing the good ideas you find?  Please share!

The Number Hunter

This week I learned about a new project that sounds awesome! I am always looking for video that inspires students to want to learn math.

Introducing The Number Hunter!

Stephanie Glen is creating a web-based TV show that’s both fun and educational. She wants to use the same idea that made science fascinating to children.   Stephanie uses Bill Nye, the science guy, as her example.  He introduced cool experiments in video and students were enticed to learn more!  

Check out The Number Hunter project!

And while you are exploring math online, peruse Stephanie's website on statistics!

it IS beautiful!

"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."  J.H.Poincare (1854-1912)

I've always enjoyed math as far back as I can remember.  I was good in math in school.  I remember other students wanting my help ... wanting my homework!  I also remember in 8th grade wanting to take Algebra 1 and my first year of a foreign language.  I requested to take both but I was told that I could not ... I was allowed to take the foreign language but not the algebra.  (I remember that incident as gender bias.)

Even though I enjoyed math as a student, I didn't see the beauty of math until much later.  As I began to attend math conferences as a teacher, I heard people talk about patterns, connections, references in math that to the best of my knowledge I wasn't taught in school.  It was in learning about the patterns and connections that I determined to share the beauty of math with my students.

One of my favorite exercises is exploring the patterns in Pascal's Triangle.  With elementary students we explore even and odd numbers - coloring them in - discovering the pattern of Sierpinski triangles.  In middle school we look at the patterns of polygonal numbers - square numbers, triangular numbers - and look for others in Pascal's Triangle.  In high school, the connection between the binomial theorem and Pascal's Triangle are noted.  At various levels we explore the connection between Fibonacci's Sequence and the Triangle ... with the challenge to discover other hidden beauty!

A favorite author I use as a resource to learn more about the beauty of mathematics is Theoni Pappas.  She has written numerous books, some of which I own, and I find her books accessible at all levels of learning.  One book I like to keep near my desk is her compendium of mathematical quotations.  I know that you can find hundreds online in the blink of an eye ... but there is something special about having a small volume of pertinent quotes on your desk!

I love to share quotes about the beauty of math with students because for so many students, math is painful and sometimes while learning the language and processes of math they miss out on the beauty!

"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. " G. H. Hardy (1877 - 1947)