Thursday, October 25, 2012

Hot Topic #2: What is School for?

Another great hot topic is answering the question, What is School for?

What a marvelous question to ask parents, teachers, and students. This really should be the primary question of everyone in our community. If we don't know what we are here for, then why do we do it? As teachers are we just here to earn a living? Can we really boil it down to a simple Mission Statement: "To graduate Responsible, Productive Citizens"?  I personally hope it's much deeper than that.  Watch this great video from Tedx to look deeper into this question:

Wednesday, October 24, 2012

Hot Topic: Is Algebra Important?

I love Math. But, Math, Algebra, and just about anything connected to it, get a bad rap from almost everyone.  There has been a war of words lately about the value of Math. It started with the New York Times article by Andrew Hacker: Is Algebra Necessary?

To say several people have responded to this Article doesn't do it justice. But, I wonder what students have to say about it. Below is a rebuttal by Hemant Meta who wrote an article in Patheos arguing the other side of the debate.  Read the New York Times Article and then the article below (I had to edit it slightly due to some inappropriate language in the comments.)  Then give me your opinion!

This is a VERY HOT TOPIC and worthy of debate!

Tomorrow, my Algebra and Geometry students will weigh in on their own blogs. I will link some of their responses. Here's a great video to get your Brain in motion!

Why Algebra is Necessary: Rebutting Andrew Hacker

July 31, 2012 By Hemant Meta ,
I teach Geometry. I’ve taught it for years. I’ll have two sections of it this year. Probably 65 kids. Every year that I’ve taught the subject, kids have freaked out at the mere mention of the word “Proof.” Without actually knowing what they are or how to do them, they want to give up immediately. And they rationalize their fear by asking me when they’re ever going to use it in life.
My response has always been something like this:

“You will probably never need to prove that two triangles are congruent to each other, but this unit isn’t really about that. What we’re doing is proving something that you only intuitively think is true. You’re using a logical, step-by-step approach, justifying every single argument you make. Furthermore, you’re only allowed to use a basic set of rules to justify your thinking. Can you explain your answers to me in a way that is easy to understand and impossible to refute?”

And then, inevitably, the next day, they forget that speech and ask me when they’re ever going to use this in life. And then I slam my head on the desk.

The worst part is that a number of math departments that I know of are pushing to de-emphasize proofs, spend less time on them, make them less rigorous, or get rid of them altogether. Which is the worst possible way to deal with the issue since, in my mind, proofs are the most important part of the class.
So you can understand my rageface as I read Andrew Hacker‘s article in the New York Times asking, “Is Algebra Necessary?

(Quick note: Andrew Hacker wrote a *wonderful* book with Claudia Dreifus calling into question how colleges are run — I can’t recommend it enough. Awesome book.)

Back to Hacker’s article, which I’m not a fan of. Here’s what he writes:

“A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.”

Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.
His argument can be boiled down to this: A lot of people suck at algebra and we hold them back because of it, but most students will never need to know the specifics of algebra to do their jobs later in life. So why put such a big emphasis on the subject?

My response is the same one I give my Geometry students: It’s not about specific calculations. It’s about being able to take a set of rules and apply them in different situations.

This idea of not teaching kids things that might be difficult and that they won’t directly use in life could justify getting rid of damn near every class. But we ought to approach them the same way as we do math. English shouldn’t be about the specific books we read — it should be about how we analyze them and what we take from them. History shouldn’t be about specific dates — it should be about the patterns and trends that emerge.

It’s hard to convey all that to students (and some teachers) and most of them will never pick up on that when they’re in school. But that doesn’t mean we should skip out on these subjects.
As Evelyn Lamb at Scientific American puts it, “Math education needs to improve, but if illiteracy were on the rise, I don’t think we’d be talking about eliminating reading from the curriculum.”

(Of course, there are also all the standard math teacher responses: Every career uses some form of math. You’re gonna have to know some basic algebra when you’re buying a house, or creating a budget, etc. Even if you don’t think you need math later in life right now, you may change careers.)

Hacker says later in the piece that requiring all students to take some form of statistics would be more worthwhile, and I agree with him, though not at the expense of ignoring core math subjects.

Art Benjamin actually gave a wonderful and really short TED talk on how schools ought to restructure their curriculums so that the pinnacle of math is Probability and Statistics instead of Calculus. I show it to my AP Stats kids the first day of school:

Benjamin is saying something not too far removed from Hacker — let’s make sure the math we’re teaching to students is relevant to our society. I agree — Statistics is far more relevant to the public discourse than Calculus — but even Benjamin is only suggesting a realignment of our priorities, not avoidance of a tough subject.
(Not to mention you really can’t do basic Prob/Stats without an understanding of basic algebra.)

One of the problems we have in the math world right now is that the standardized tests that are used to evaluate schools and teachers force students to focus on the wrong things. They focus rote calculations instead of critical thinking. Hell, there’s an entire test-prep industry built on helping students get high scores without necessarily knowing all the material.

But, again, the solution to all of this is not avoiding the subject. It’s teaching it better.

For example, one of the things my department is working on this coming year is getting away from spending all our time on skills that just require mindless work — plugging and chugging — and spending more time in class on one or two problems that require a lot more thought. Let’s see how far the students can get on their own (or with a group) and help them when they get stuck. That would force them to think in a much different way, which gets to the heart of why we teach math.

We also have to revise our teaching because we live in a world with graphing calculators and Wolfram Alpha — and we want students to use them. So let’s teach them when and how to use those tools. Again — less regurgitation of skills, more critical thinking.

Will it still be tough? Absolutely. But if we don’t challenge students, why should we expect them to work hard and push themselves? Math isn’t supposed to be easy. But it is logical. And the students who understand the rules tend to do pretty damn well.

A few more notes.

Hacker writes this:

What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey…
It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.

Riiight. Reading Jane Eyre and studying the periodic table doesn’t help with any of that either. Should we kick English and Chemistry to the curb, too?

Does anyone know what that formula is? Because it’s actually pretty amazing. It’s Euclid’s formula for generating Pythagorean triples (like 3,4,5 and 5,12,13) — it even resembles the Pythagorean Theorem, c² = a² + b² — and it can be very useful if you’re studying Geometry. But if you just think of it as a series of variables without any context, as Hacker does, it’s pretty meaningless.

Andy Soffer elaborates on that formula:
To be fair, I don’t think we should expect non-mathematicians to recognize this formula. It’s beyond what I think is necessary to be a well-rounded citizen. But I do think we should expect the average American to be able to do the basic algebraic manipulations to prove this identity. This is the sort of mathematical literacy I would deem the rough equivalent of being able read, or being able to write in complete sentences.

Hacker also says he thinks all students should be able to do things like “long division,” that they should know basic arithmetic skills. But the students who don’t do well in algebra usually struggle precisely because they don’t know basic arithmetic.
Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.

Wednesday, October 17, 2012

Parent Teacher Conferences! -- Wed. Oct. 24th

A week from tonight, October 24th, will be GHS Parent Teacher Conferences. PLEASE, come!

I really would love to meet with every students parents. I love ALL my students and have great things to say about all of them. Parents don't get to hear those things very often and students need to hear those things. But, I also want parents to come and see what we're doing. From the guitar project to the twitter project, I want them to see what we are doing to bring math to life in the 21st century. Come and ask me about khan Academy, twitter, green car projects, blogs, powerschool, homework, and how we are trying to teach criticsl thinking and collaborationI at GHS. I want to help connect parents with their students on Khan, read this blog, and open the doors for them to be involved on a daily basis with educating their students at GHS!

SO, students and community members, get the word out. Parent Teacher conferences are Wednesday, October 24th from 3:30 - 7:30. You can call for a specific appointment or just drop in.

You can contact me at or call the school.  The phone number is 357-4114. My extension is : 3217

Thursday, October 11, 2012

Hard Work Matters! Great Week!

Tomorrow caps off a great week in my Math Classes. My students continue to amaze me with their hard work and dedication. I was raised that hard work pays off in everything you do. My students that are working hard are doing a great job. MOST of my students ARE working hard. I have only a few that are struggling academically. The number one reason for failure in my class is not doing your work.  Parents can check on students to see how HARD they are working. Just get on the school website and check the grades. If you start seeing a bunch of zeros you can bet they are NOT working hard.   Here's a recap of our week:


We spent a lot of time on KHAN ACADEMY this week working on Linear Equations, Slopes, Y-intercepts, and X-intercepts. Tomorrow, we will take a mini break from skill work and apply what we've learned about slope. We are having a "Slope Scavenger Hunt". Students will break up into groups and measure slopes. I have a list of 10 slopes for them to measure on our campus. The TEAM of students that accurate complete the list in the shortest amount of time win. My lovely wife has baked a great batch of cookies for the winning team!
I know students LOVE these equations. But, if we want students to be able to evaluate complex data and statistics they will need to be comfortable with linear relationships. We spend an enormous amount of time on becoming comfortable with linear equations. 


We have had a busy week with constructions this week. Students are getting more comfortable with the compass and straight edge. We started out just copying segments and angles. We concluded today with constructing a Square, Pentagon, and Hexagon. Tomorrow Students will design a "Personal Logo" using only a compass and straight edge. We haven't spent ANY time on Khan this week as they do not have a section dealing with constructions. The students have done a great job learning how to follow step by step instructions. I was asked the famous question "When are we ever going to use this?" In my recent discussion with other teachers, we all find students can not follow directions very well. Learning GEOMETRIC CONSTRUCTIONS is a fun way to help students learn to follow step by step instructions. When I teach this it always reminds me of my days "Helping Santa" put together toys at Christmas. We had many a late night following step by step instructions. I can't think of too many jobs where employees aren't required to follow a detailed set of procedures.

Looking forward to a FABULOUS FRIDAY!

Monday, October 8, 2012

Should students be allowed to fail!

We had a great week last week in Algebra and Geometry ending with our first twitter project. Students did a nice job of picking apart the CDC report on Student Drinking and Driving. We had a great class and twitter discussion.

In Algebra we started work with Linear Equations, slopes, graphing, and the coordinate plane. This week we continue building on that while learning to manipulate the equations.

In Geometry we finally got through areas, perimeters, and circumference. After a little work everybody was successful on the assessment. We now get to move on to constructions. I love working with a compass and straightedge.

In Algebra, we had a discussion about "Should teachers let students fail?" Im not talking about students who work hard but still struggle. I'm talking about students who choose to fail. Teachers really struggle with students who just WON'T work and fail because of it. Most teachers at GHS won't fail a student that works hard. They give opportunity after opportunity to be successful. Math can be difficult and I provide many different methods for students to learn the material. I use tests and assessments as only one of many ways To demonstrate students have learned a concept. Projects, daily work, writing, collaboration, communication, engagement, and organization are all keys to being successful in my class. You could be weak in one or two areas, but still be successful.

The students all shared my thoughts that most students have to work pretty hard at failing in school. Several mentioned we should let them fail and suffer the consequences. But, I just can't give up looking for ways to help them see success. I love the challenge!

I am fortunate to have many great students who work hard in my classes. I love going to school and love the opportunity to work with my colleagues!

Thursday, October 4, 2012

Twitter Project GHS Math tomorrow!

I am nervous and excited about my first ever Math Twitter project tomorrow in my Math classes.

We will analyze a new report from the CDC about Teen Drnking and Driving. We will debate, comment, critique, and question this report and the data collected. We will attack the bold claim made by the CDC that student drinking and driving has decreased by 54% over the last 20 years. All of this debate will take place over Twitter.

Math class?

I know many people might question the VALUE of this project for Math class. "It has nothing to do with our current study of Linear Equations or Geometry." Or Does it? Besides the rich data in the report, the abstract also talks about linear and quadratic relationships of the data. Where else should students learn how to analyze data and apply reasoning to REAL life? They might need to know            y = mx + b for the state assessment, but they need to know how to analyze data to make informed decisions as future citizens in our state and country. At GHS we have our mission statement "To graduate responsible, productive citizens." In my opinion, this helps fulfill that mission. If you get a chance join in the conversation!


Twitter is the second largest social media site on the Internet. I want my students to have an AUTHENTIC audience. I don't want them limited to "performing" just for me. Commenting in 140 characters will take some thought!

Even though this is a serious topic, it will be fun to communicate using the Internet, while sitting in the same room.

Wish us Luck!

Monday, October 1, 2012

This Week - Week #5 in Review!

Now that the Dekalb County Fair is over, Homecoming is behind us, and College Go Week has gone, we can actually get back to MATH! I love all the festivities at school, but they do have a tendency to distract students.

Algebra 1
I am in the middle of grading the "Green Car Projects" that were turned in on Friday. I loved this project and what it trained our students to do. It is so important for "Consumers" to research and analyze products before making major purposes. With the internet, we have access to such a vast amount of information. We have no excuse for making a poor choice when purchasing Cars, Homes, or other "Big Ticket" items.

This week we will start with reviewing for our second Assessment. The Assessment will take place tomorrow and we will collect Data Notebooks. Students should review Khan Academy skills practice sets on Absolute Value, InEqualities, Multi-Step Equations, and solving for a variable.

We will be jumping into MORE Linear Equations and Graphs of Lines. This has to be one of the most useful units we will learn about all year. Data Graphs are everywhere and a clear understanding of Lines, Slopes, and Linear Relationships is CRITICAL.

Here are the Khan Academy Skills we will be working on in this next unit:

          Graphing Points
          Graphing Points and Naming Quadrants
          Points on the Coordinate Plane
          Identifying linear relationships
          Indentifying slope of a line
          Line graph intuition
          Solving for the y-intercept
          Solving for the x-intercept
          Equations from tables
          Slope Intercept form
          Point slope form
          Converting between slope-intercept and standard form

We are also to the point of our next Assessment. We will review today and Assess tomorrow. Data Notebooks will be collected on TUESDAY. From there, we will do some work with constructions using Compass and Straightedge. Then we will begin our first BIG PBL PROJECT.

Khan Academy does not have any skill work for constructions. HOWEVER, we will continue to work on our Algebra and Math Skills in between working on Constructions and our PBL project.

My classes are doing GREAT! Just remember to KEEP WORKING HARD. Students need to keep notebooks up to date. Weekly Progress Reports are graded on the amount of time Students work on Skills IN-CLASS. If we work 60 minutes in a week, a student will need at least 54 minutes to get an A. Life Skills are graded on participation in class. That MEANS how much a student focuses on MATH during class time. WE DO NOT ASSIGN HOMEWORK AS LONG AS STUDENTS WORK HARD IN CLASS!

I am greatly impressed with the Positive Attitudes of the students in my classes. I look forward to learning with you EVERY DAY!