Wednesday, March 30, 2016

Algorithms and Losing Control

On my way to the gym this morning I listened to yet another story on NPR about the FBI/Apple controversy surrounding accessing the iPhone of the San Bernardino terrorists. Quick synopsis - Apple refused, FBI found a 3rd party who was able to create their own algorithm to hack into the phone, FBI dropped case against Apple. But - everyone is worried.  Will the FBI share this code-breaking algorithm with other law enforcement? Will we all be vulnerable now to some outside person accessing the privacy of our smartphones?!

Legal issues aside, what I find interesting is the fact that an algorithm unlocked the information. Or algorithms created the 'locked phone' in the first place. As a math person, it's always  fascinating to think about how algorithms create so much of what is around us, and while I don't understand it myself, there are people out there who do.  People who can create a code to break into a locked phone. Or an algorithm to pick stocks or predict weather.  It's really incredible. A little mind boggling.

With this on my mind, I was excited to actually find a Ted Talk specifically on algorithms and the world around us. Seemed sort of ironic - though, it was probably a Google algorithm that matched my search of the NPR story to other stories and resources that contain algorithms.  Spooky!! In fact - the talk, by Kevin Slavin, addresses this very fact - that algorithms and coding are responsible for some of our decisions (or many).  So - are we in control or are the algorithms controlling us?

Watch the Ted Talk and freak yourself out too!

Tuesday, March 22, 2016

Common Core is NOT the same as Standardized Testing

I have read a couple articles of late that have kind of pissed me off.  Mainly because they perpetuate the ideas that 1) The Common Core State Standards are handed down from the Federal Government, and 2) that the CCSS are the driving force behind Standardized Testing.  While there are connections, both claims are a complete disservice to the purpose behind and the reason for The Common Core State Standards. And they completely ignore the fact that Standardized Testing is actually controlled by testing companies and publishing companies.

I've already posted on this before - "What People Think Is Common Core ISN'T" and "Common Core, It's NOT the Devil" so I apologize now for being repetitive. One article I read last night, entitled "What's the largest number you can represent with 3 digits? Nope. It's not 999."  is a great article. I agree with everything the author said and applaud his sticking by his daughter, the second teacher, and the fact that he forced the standardized testing company to change their answers.  Awesome.  Then I saw the last line: "don't let common core stand in the way of  your own children's education".  Sigh.  IT"S NOT THE COMMON CORE that's doing this - it's publishing companies, it's testing companies, it's misunderstanding and lack of training of teachers.

As I've written before, the Common Core actually represents problem solving, critical thinking, perseverance, multiple solutions (as this author was demonstrating his daughter was showing), communication, multiple pathways.  It's all about unique minds and coming to mathematical understanding from different perspectives.  Read the standards.  Especially the Standards for Mathematical Practice.  What the above article was demonstrating was the fact that the teacher was NOT following Common Core Practices, whether through ignorance or more likely, through the pressure of textbooks publishers and standardized testing companies to "standardized" the Common Core, and thus in fact become something completely different than what the Common Core represents. Let's go back to my two previous postings....what people think is Common Core ISN'T - it comes back to our testing culture and a need to standardize so we can "assess" students quickly, and in the process, take out all the problem-solving, uniqueness, critical thinking that is the essence of the common core.

Here are some facts about the Common Core:

  1. State education chiefs and governors in 48 states came together to develop the Common Core, a set of clear college- and career-ready standards for kindergarten through 12th grade in English language arts/literacy and mathematics. Today, 42 states and the District of Columbia have voluntarily adopted and are working to implement the standards, which are designed to ensure that students graduating from high school are prepared to take credit bearing introductory courses in two- or four-year college programs or enter the workforce.
  2. States led the development of the Common Core State Standards. In 2009, state leaders, including governors and state commissioners of education from 48 states, two territories and the District of Columbia, came together and decided to develop common, college- and career-ready standards in mathematics and English language arts. They worked through their membership organizations – the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) –  to accomplish this. The development process included defining expectations for what every child should know and be able to do when they graduate from high school and then creating content standards for grades K-12 aligned with these expectations. States relied on workgroups of educators, representatives of higher education and other experts to write the standards with significant input from the public in 2009 and 2010. States then appointed a validation committee to review the final standards. The federal government was not involved in the development of the standards. The final standards were published in June 2010 and available for each state to review, consider and voluntarily adopt. 
  3. Adoption of the standards is voluntary. It is up to each state and territory to decide if they choose to adopt the Common Core State Standards as their state educational standards in English language arts and mathematics. States can tailor the standards to address their needs. Here is a map showing the states that have adopted the standards.
The standards are voluntary, with the idea that if all states had the same standards it would be easier for students to be compared state-to-state and to ensure that all students, no matter where they live, were getting an equal and rigorous education. Notice - nothing about the Federal Government.  The Federal Government did encourage adoption and funding with Race-to-the-Top money if states adopted the Common Core, but not required. And NCLB did require standardized testing of all students, which is the 'standardization' push of the Common Core Standards, which are difficult to assess in a standardized test.  Standardized tests are NOT Common Core.

Standardized testing - states realized they needed to assess and that they needed some help with
standardized testing aligned to The Common Core. States got together to create consortiums, such as PARCC and Smarter Balance Assessments.  These were led by Pearson (PARCC) and a "public agency" (Smarter Balance Assessment) and state leaders who opted to join the consortiums.  These assessments are voluntary and there have been issues with both. There are currently only 15 states still in Smarter Balance and only 11 left in PARCC.  Many states have dropped out. 

With the adoption of ESSA, where states have more control over assessments, there is going to be a change in which standardized tests are used to assess students. But they are not "Common Core".  ACT, SAT, NAEP - the most commonly used now, are definitely NOT Common Core. In fact - true assessment of Common Core should not be standardized, especially when keeping the mathematical practices in check.  There-in lies the problem. We are trying to standardized standards that are meant to help students become problem-solvers, critical thinkers, and communicators. You can't demonstrate that on multiple-choice tests where one correct answer is the norm.  So - rather than blaming Common Core, blame the 'standardized' way of thinking that forces teachers to teach to a standardized test, accept only "one" answer, or force ways of thinking on students when they should be encouraging uniqueness and multiple pathways. In order to change the way students learn, we need to change the way we assess or we are always going to be forcing students into one or two ways of thinking so they can 'pass the test'. 


Wednesday, March 2, 2016

What is the "Math Path" We Should Encourage Students to Take?

I read this article the other day by Dana Goldstein, "Down with Algebra II!", which describes professor Andrew Hackers views on mathematics, and how the push for STEM, higher math like Algebra II, is actually creating a the failure and dropout rates we are seeing because it is pushing students into mathematics that is not necessary for their future endeavors and "destroying a tremendous amount of talent". The math requirements in high school and college are "highly irrational".

And then my friend sent me the same exact article via Facebook and asked my opinion. (This is what happens when your friends know you are a math person!). So - what is my opinion? I have to say, I completely agree with Andrew Hacker. In fact - I have written about it before a few times: Math Curriculum - What should we be teaching?; Financial Literacy - Real-world math, REALLY; Let's teach probability & Statistics - We need it! 

Don't get me wrong - I think Algebra II and higher level math is important.  I believe in the Common Core Standards, which recommend higher mathematical concepts.  However - NOT for everyone. My friend who sent me the FB link, has a student with a learning disability who completely struggles in math. She was concerned because if Algebra II is a requirement, she knows her son will struggle, probably not get the grade needed, which will then hurt his chances of getting into a college of his choice. He is NOT planning to go into a field where he would need Algebra II, or Calculus.  Which is true for many students. But - in our traditional curriculum, even with the Common Core, we push students along the following path: Algebra, Geometry, Algebra II, Pre-Calculus, Calculus.  Maybe some Trig.  Rarely do we push them into Probability & Statistics, and since Computer Science is usually NOT allowed as a math credit, we don't push them there either.  And Personal Finance? Not even an offering in most places.

I will use my daughters as examples.  The oldest is an art person - lives, eats, breaths art.  If she could
Example Oldest Daughters Art - Acrylic 
draw all day (which she does), she would be happy and satisfied, with the occasional break to eat. The younger - well, she is still a conundrum, but she is brilliant with math and science.  She just gets it.  She thinks different. When it came to what to take after Algebra II (required), it was a no brainer for the younger one to go into precalculus and calculus. She needed the challenge.  However I told my older daughter she should take statistics.  It would be more relevant to her more artsy/business direction (advdertising). Let me tell you - her counselor was NOT happy.  Kept trying to push her towards Pre-calculus instead so she would get into "college". NO.  This daughter would have done horrible in Pre-calculus - she was not interested in it, was not planning to use this mathematics in her future endeavors, so why should she be forced down this path?  Well - we went against counselors wishes and took statistics, which she absolutely loved (great teacher) and totally excelled in.  It was relevant, real-world, hands-on and - pertinent to what she does now.  Perfect match.  But - it was NOT on the recommended path so we had to fight for her right to take it.  My point - two very different daughters, two very different personalities and interests, and therefore they should have two very different pathways.

I completely agree we need more students interested in STEM careers, however, not every student needs to be pushed here, especially if their interests lie in arts, history, business, computer gaming, etc.  All students need math - and I am a big believer of math every year through grade 12. But - just different math. What I think, especially in this age of "personalized learning", is there needs to be choice in mathematics, and not the constant push to force all students down the same path, a path that for many is unnecessary and a road to failure. I definitely want students to learn math - and I truly believe in the Common Core State Standards - which emphasize problem solving, real-world application, critical thinking and conceptual understanding.  All of these goals can be accomplished with other math choices. If we had other pathways for mathematics, we might actually find students developing an interest in math and pursuing higher level courses of their own free will.

A lot of districts will say they don't have the funding to offer more math choices. With online
Andres Marti Teaching Statistics w/TinkerPlots
learning that is not an excuse, as long as districts are willing to accept credits students take online from other places. Additionally, districts/states need to rethink the math requirements and what courses count towards a math credit.  Thankfully, this seems to be coming up more and more, but courses like computer science should count as math credit (to replace Algebra II or Calculus), Personal Finance courses should be offered first of all, and should also count as a math credit. How does this work with Common Core State Standards and other standards? It shouldn't impact those at all - if students do take Algebra, Algebra II , Statistics, then the content standards should be followed. The Mathematical Practices should be followed no matter what courses you take. But - what is 'required' for math credit - THAT's what should be rethought. Let's make learning about what is going to help a student acquire the skills they need to pursue the career path they want and be productive members of society. Personal Finance would go a lot further towards that goal for all students than Algebra II, don't you think?

What is my ideal math menu?

1) Students should have at least 4 math credits to graduate high school.  Math is important!
2) What are some required courses?

  • Basic Algebra (abstract thinking is important and useful to everyone)
  • Geometry (this helps with logic, spatial reasoning, etc.)
  • Personal Finance (yes - EVERYONE)
3) What are some optional courses that count as MATH credit? (not exhaustive)
  • Computer Science - all kinds (coding, robotics, gaming, etc.)
  • Probability & Statistics (voting, sampling, etc...important for being a functioning person in todays' society)
  • Advanced Algebra (Algebra II?)
  • PreCalculus
  • Calculus (A&B)
  • Trigonometry
  • Math for Medicine (i.e. for those interested in nursing or doctors)
  • Accounting
There are more that could be added to the optional courses list obviously - this is just a smattering. But - what matters here is there is choice. And based on a students interests, they should be given the choice.